Program to multiply two matrices

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Given two matrices, the task is to multiply them. Matrices can either be square or rectangular:

Examples:

(Square Matrix Multiplication)

Input: mat1[m][n] = { {1, 1}, {2, 2} }
mat2[n][p] = { {1, 1}, {2, 2} }
Output: result[m][p] = { {3, 3}, {6, 6} }

(Rectangular Matrix Multiplication)

Input: mat1[3][2] = { {1, 1}, {2, 2}, {3, 3} }
mat2[2][3] = { {1, 1, 1}, {2, 2, 2} }
Output: result[3][3] = { {3, 3, 3}, {6, 6, 6}, {9, 9, 9} }

Multiplication of two Square or Rectangular Matrices:

The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2.

Output of multiplication of Matrix-1 and Matrix-2, results with equal to the number of rows of Matrix-1 and the number of columns of Matrix-2 i.e. rslt[R1][C2]

Below is the implementation of the multiplication of two matrices:

C

// C program to multiply two matrices 
  
#include <stdio.h> 
#include <stdlib.h> 
  
// Edit MACROs here, according to your Matrix Dimensions for 
// mat1[R1][C1] and mat2[R2][C2] 
#define R1 2 // number of rows in Matrix-1 
#define C1 2 // number of columns in Matrix-1 
#define R2 2 // number of rows in Matrix-2 
#define C2 2 // number of columns in Matrix-2 
  
void mulMat(int mat1[][C1], int mat2[][C2]) 
{ 
    int rslt[R1][C2]; 
  
    printf("Multiplication of given two matrices is:\n"); 
  
    for (int i = 0; i < R1; i++) { 
        for (int j = 0; j < C2; j++) { 
            rslt[i][j] = 0; 
  
            for (int k = 0; k < R2; k++) { 
                rslt[i][j] += mat1[i][k] * mat2[k][j]; 
            } 
  
            printf("%d\t", rslt[i][j]); 
        } 
  
        printf("\n"); 
    } 
} 
  
// Driver code 
int main() 
{ 
    // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these 
    // values in MACROs) 
    int mat1[R1][C1] = { { 1, 1 }, 
                         { 2, 2 } }; 
  
    int mat2[R2][C2] = { { 1, 1 }, 
                         { 2, 2 } }; 
  
  
    if (C1 != R2) { 
        printf("The number of columns in Matrix-1  must be "
               "equal to the number of rows in "
               "Matrix-2\n"); 
        printf("Please update MACROs value according to "
               "your array dimension in "
               "#define section\n"); 
  
        exit(EXIT_FAILURE); 
    } 
  
      // Function call 
    mulMat(mat1, mat2); 
  
    return 0; 
} 
  
// This code is contributed by Manish Kumar (mkumar2789)

C++

// C++ program to multiply two matrices 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Edit MACROs here, according to your Matrix Dimensions for 
// mat1[R1][C1] and mat2[R2][C2] 
#define R1 2 // number of rows in Matrix-1 
#define C1 2 // number of columns in Matrix-1 
#define R2 2 // number of rows in Matrix-2 
#define C2 2 // number of columns in Matrix-2 
  
void mulMat(int mat1[][C1], int mat2[][C2]) 
{ 
    int rslt[R1][C2]; 
  
    cout << "Multiplication of given two matrices is:\n"; 
  
    for (int i = 0; i < R1; i++) { 
        for (int j = 0; j < C2; j++) { 
            rslt[i][j] = 0; 
  
            for (int k = 0; k < R2; k++) { 
                rslt[i][j] += mat1[i][k] * mat2[k][j]; 
            } 
  
            cout << rslt[i][j] << "\t"; 
        } 
  
        cout << endl; 
    } 
} 
  
// Driver code 
int main() 
{ 
    // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these 
    // values in MACROs) 
    int mat1[R1][C1] = { { 1, 1 }, 
                         { 2, 2 } }; 
  
    int mat2[R2][C2] = { { 1, 1 }, 
                         { 2, 2 } }; 
  
    if (C1 != R2) { 
        cout << "The number of columns in Matrix-1  must "
                "be equal to the number of rows in "
                "Matrix-2"
             << endl; 
        cout << "Please update MACROs according to your "
                "array dimension in #define section"
             << endl; 
  
        exit(EXIT_FAILURE); 
    } 
  
      // Function call 
    mulMat(mat1, mat2); 
  
    return 0; 
} 
  
// This code is contributed by Manish Kumar (mkumar2789)

Java

// C++ program to multiply two matrices 
  
import java.io.*; 
import java.util.*; 
  
class GFG { 
  
    static int R1 = 2; // number of rows in Matrix-1 
    static int C1 = 2; // number of columns in Matrix-1 
    static int R2 = 2; // number of rows in Matrix-2 
    static int C2 = 2; // number of columns in Matrix-2 
  
    // This function multiplies mat1[][] 
    // and mat2[][], and stores the result 
    // in res[][] 
    static void mulMat(int[][] mat1, int[][] mat2) 
    { 
        // To store result 
        int[][] rslt = new int[R1][C2]; 
        System.out.println( 
            "Multiplication of given two matrices is:"); 
        int i, j, k; 
        for (i = 0; i < R1; i++) { 
            for (j = 0; j < C2; j++) { 
                rslt[i][j] = 0; 
                for (k = 0; k < R2; k++) 
                    rslt[i][j] += mat1[i][k] * mat2[k][j]; 
                System.out.print(rslt[i][j] + " "); 
            } 
            System.out.println(""); 
        } 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        int[][] mat1 = { { 1, 1 }, 
                         { 2, 2 } }; 
  
        int[][] mat2 = { { 1, 1 }, 
                         { 2, 2 } }; 
  
  
        if (C1 != R2) { 
            System.out.println( 
                "The number of columns in Matrix-1  must be equal to the number of rows in Matrix-2"); 
            System.out.println( 
                "Please update the global variables according to your array dimension"); 
        } 
        else { 
            
              // Function call 
            mulMat(mat1, mat2); 
        } 
    } 
} 
// This code is contributed by shruti456rawal

Python3

# Python3 program to multiply two matrices 
  
  
def mulMat(mat1, mat2, R1, R2, C1, C2): 
    # List to store matrix multiplication result 
    rslt = [[0, 0, 0, 0], 
            [0, 0, 0, 0], 
            [0, 0, 0, 0], 
            [0, 0, 0, 0]] 
  
    for i in range(0, R1): 
        for j in range(0, C2): 
            for k in range(0, R2): 
                rslt[i][j] += mat1[i][k] * mat2[k][j] 
  
    print("Multiplication of given two matrices is:") 
    for i in range(0, R1): 
        for j in range(0, C2): 
            print(rslt[i][j], end=" ") 
        print("\n", end="") 
  
  
# Driver code 
if __name__ == '__main__': 
    R1 = 2
    R2 = 2
    C1 = 2
    C2 = 2
      
    # First matrix. M is a list 
    mat1 = [[1, 1], 
           [2, 2]] 
      
    
    # Second matrix. N is a list 
    mat2 = [[1, 1], 
           [2, 2]] 
  
    if C1 != R2: 
        print("The number of columns in Matrix-1  must be equal to the number of rows in " + "Matrix-2", end='') 
        print("\n", end='') 
        print("Please update MACROs according to your array dimension in #define section", end='') 
        print("\n", end='') 
    else: 
        # Call matrix_multiplication function 
        mulMat(mat1, mat2, R1, R2, C1, C2) 
  
# This code is contributed by Aarti_Rathi 

C#

// C# program to multiply two matrices 
  
using System; 
  
class GFG { 
  
    static int R1 = 2; // number of rows in Matrix-1 
    static int C1 = 2; // number of columns in Matrix-1 
    static int R2 = 2; // number of rows in Matrix-2 
    static int C2 = 2; // number of columns in Matrix-2 
  
    // This function multiplies mat1[][] 
    // and mat2[][], and stores the result 
    // in res[][] 
    static void mulMat(int[, ] mat1, int[, ] mat2) 
    { 
        // To store result 
        int[, ] rslt = new int[R1, C2]; 
        Console.WriteLine( 
            "Multiplication of given two matrices is:"); 
        int i, j, k; 
        for (i = 0; i < R1; i++) { 
            for (j = 0; j < C2; j++) { 
                rslt[i, j] = 0; 
                for (k = 0; k < R2; k++) 
                    rslt[i, j] += mat1[i, k] * mat2[k, j]; 
                Console.Write(rslt[i, j] + "\t"); 
            } 
            Console.WriteLine(); 
        } 
    } 
  
    // Driver code 
    public static void Main() 
    { 
        int[, ] mat1 = { { 1, 1 }, 
                         { 2, 2 } }; 
  
        int[, ] mat2 = { { 1, 1 }, 
                         { 2, 2 } }; 
  
        if (C1 != R2) { 
            Console.WriteLine( 
                "The number of columns in Matrix-1  must be equal to the number of rows in Matrix-2"); 
            Console.WriteLine( 
                "Please update MACROs according to your array dimension in #define section"); 
        } 
        else { 
            mulMat(mat1, mat2); 
        } 
    } 
} 
  
// This code is contributed by Aarti_Rathi

Javascript

var R1 = 2; 
// number of rows in Matrix-1 
var C1 = 2; 
// number of columns in Matrix-1 
var R2 = 2; 
// number of rows in Matrix-2 
var C2 = 2; 
// number of columns in Matrix-2 
// This function multiplies mat1[][] 
// and mat2[][], and stores the result 
// in res[][] 
function mulMat(mat1, mat2) 
{ 
    // To store result 
    var rslt = Array(R1).fill(0).map(()=>new Array(C2).fill(0)); 
    console.log("Multiplication of given two matrices is:"); 
    var i = 0; 
    var j = 0; 
    var k = 0; 
    for (i = 0; i < R1; i++) 
    { 
        for (j = 0; j < C2; j++) 
        { 
            rslt[i][j] = 0; 
            for (k = 0; k < R2; k++) 
            { 
                rslt[i][j] += mat1[i][k] * mat2[k][j]; 
            } 
            console.log(rslt[i][j] + " "); 
        } 
        console.log(""); 
    } 
} 
// Driver program 
  
var mat1 = [[1, 1], [2, 2]]; 
var mat2 = [[1, 1], [2, 2]]; 
  
if (C1 != R2) 
{ 
    console.log("The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2"); 
    console.log("Please update the global variables according to your array dimension"); 
} 
else 
{ 
    mulMat(mat1, mat2); 
} 
  
// This code is contributed by Aarti_Rathi

Output

Multiplication of given two matrices is:
3    3    
6    6

Time complexity: O(R1 * C2 * R2) for given matrices mat1[R1][C1] and mat2[R2][C2]
Auxiliary space: O(R1 * C2)

Multiplication of Rectangular Matrices using Pointers in C/C++:

To solve the problem follow the below idea:

We use pointers in C/C++ to multiply matrices

Prerequisite: How to pass a 2D array as a parameter in C?

Below is the implementation of the above approach:

C++

// C++ program to multiply two 
// rectangular matrices 
#include <bits/stdc++.h> 
using namespace std; 
  
// Multiplies two matrices mat1[][] 
// and mat2[][] and prints result. 
// (m1) x (m2) and (n1) x (n2) are 
// dimensions of given matrices. 
void multiply(int m1, int m2, int mat1[][2], int n1, int n2, 
              int mat2[][2]) 
{ 
    int x, i, j; 
    int res[m1][n2]; 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            res[i][j] = 0; 
            for (x = 0; x < m2; x++) { 
                *(*(res + i) + j) += *(*(mat1 + i) + x) 
                                     * *(*(mat2 + x) + j); 
            } 
        } 
    } 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            cout << *(*(res + i) + j) << " "; 
        } 
        cout << "\n"; 
    } 
} 
  
// Driver code 
int main() 
{ 
    int mat1[][2] = { { 1, 1 }, { 2, 2 } }; 
    int mat2[][2] = { { 1, 1 }, { 2, 2 } }; 
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2; 
  
    // Function call 
    multiply(m1, m2, mat1, n1, n2, mat2); 
    return 0; 
} 
  
// This code is contributed 
// by Akanksha Rai(Abby_akku)

C

// C program to multiply two rectangular matrices 
#include <stdio.h> 
  
// Multiplies two matrices mat1[][] and mat2[][] 
// and prints result. 
// (m1) x (m2) and (n1) x (n2) are dimensions 
// of given matrices. 
void multiply(int m1, int m2, int mat1[][m2], int n1, 
              int n2, int mat2[][n2]) 
{ 
    int x, i, j; 
    int res[m1][n2]; 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            res[i][j] = 0; 
            for (x = 0; x < m2; x++) { 
                *(*(res + i) + j) += *(*(mat1 + i) + x) 
                                     * *(*(mat2 + x) + j); 
            } 
        } 
    } 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            printf("%d ", *(*(res + i) + j)); 
        } 
        printf("\n"); 
    } 
} 
  
// Driver code 
int main() 
{ 
    int mat1[][2] = { { 1, 1 }, { 2, 2 } }; 
    int mat2[][2] = { { 1, 1 }, { 2, 2 } }; 
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2; 
  
    // Function call 
    multiply(m1, m2, mat1, n1, n2, mat2); 
    return 0; 
}

Java

// JAVA program to multiply two 
// rectangular matrices 
import java.io.*; 
import java.lang.*; 
import java.util.*; 
  
// Multiplies two matrices mat1[][] 
// and mat2[][] and prints result. 
// (m1) x (m2) and (n1) x (n2) are 
// dimensions of given matrices. 
public class GFG { 
  public static void multiply(int m1, int m2, 
                              int mat1[][], int n1, 
                              int n2, int mat2[][]) 
  { 
    int x, i, j; 
    int res[][] = new int[m1][n2]; 
    for (i = 0; i < m1; i++) { 
      for (j = 0; j < n2; j++) { 
        res[i][j] = 0; 
        for (x = 0; x < m2; x++) { 
          res[i][j] += mat1[i][x] * mat2[x][j]; 
        } 
      } 
    } 
    for (i = 0; i < m1; i++) { 
      for (j = 0; j < n2; j++) { 
        System.out.print(res[i][j] + " "); 
      } 
      System.out.println(); 
    } 
  } 
  
  // Driver code 
  public static void main(String[] args) 
  { 
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2; 
    int mat1[][] = new int[][] { { 1, 1 }, { 2, 2 } }; 
    int mat2[][] = new int[][] { { 1, 1 }, { 2, 2 } }; 
  
    // Function call 
    multiply(m1, m2, mat1, n1, n2, mat2); 
  } 
} 
  
// This code is contributed by ishankhandelwals.

Python3

# Python program to multiply two 
# rectangular matrices 
  
# Multiplies two matrices mat1[][] 
# and mat2[][] and prints result. 
# (m1) x (m2) and (n1) x (n2) are 
# dimensions of given matrices. 
def multiply(m1, m2, mat1, n1, n2, mat2): 
    res = [[0 for x in range(n2)] for y in range(m1)] 
    for i in range(m1): 
        for j in range(n2): 
            res[i][j] = 0
            for x in range(m2): 
                res[i][j] += mat1[i][x] * mat2[x][j] 
    for i in range(m1): 
        for j in range(n2): 
            print(res[i][j], end=" ") 
        print() 
  
# Driver code 
m1 = 2
m2 = 2
n1 = 2
n2 = 2
mat1 = [[1, 1], [2, 2]] 
mat2 = [[1, 1], [2, 2]] 
  
# Function call 
multiply(m1, m2, mat1, n1, n2, mat2) 
  
# This code is contributed by Tapesh(tapeshdua420) 

C#

// C# program to multiply two 
// rectangular matrices 
using System; 
  
class Program { 
    // Driver code 
    static void Main(string[] args) 
    { 
        int m1 = 2, m2 = 2, n1 = 2, n2 = 2; 
        int[, ] mat1 = new int[, ] { { 1, 1 }, { 2, 2 } }; 
        int[, ] mat2 = new int[, ] { { 1, 1 }, { 2, 2 } }; 
  
        // Function call 
        multiply(m1, m2, mat1, n1, n2, mat2); 
    } 
  
    // Multiplies two matrices mat1[][] 
    // and mat2[][] and prints result. 
    // (m1) x (m2) and (n1) x (n2) are 
    // dimensions of given matrices. 
    static void multiply(int m1, int m2, int[, ] mat1, 
                         int n1, int n2, int[, ] mat2) 
    { 
        int x, i, j; 
        int[, ] res = new int[m1, n2]; 
        for (i = 0; i < m1; i++) { 
            for (j = 0; j < n2; j++) { 
                res[i, j] = 0; 
                for (x = 0; x < m2; x++) { 
                    res[i, j] += mat1[i, x] * mat2[x, j]; 
                } 
            } 
        } 
        for (i = 0; i < m1; i++) { 
            for (j = 0; j < n2; j++) { 
                Console.Write(res[i, j] + " "); 
            } 
            Console.WriteLine(); 
        } 
    } 
} 
  
// This code is contributed by Tapesh(tapeshdua420)

Javascript

// JS program to multiply two 
// rectangular matrices 
// Multiplies two matrices mat1[][] 
// and mat2[][] and prints result. 
// (m1) x (m2) and (n1) x (n2) are 
// dimensions of given matrices. 
function multiply(m1, m2, mat1, n1, n2, mat2) { 
    let x, i, j; 
    let res = [[0, 0], [0, 0]]; 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            // res[i][j] = 0; 
            for (x = 0; x < m2; x++) { 
                res[i][j] += (mat1[i][x] * mat2[x][j]) 
            } 
        } 
    } 
    for (i = 0; i < m1; i++) { 
        for (j = 0; j < n2; j++) { 
            console.log(res[i][j]); 
        } 
    } 
} 
  
// Driver code 
let mat1 = [[1, 1], [2, 2]]; 
let mat2 = [[1, 1], [2, 2]]; 
let m1 = 2, m2 = 2, n1 = 2, n2 = 2; 
  
// Function call 
multiply(m1, m2, mat1, n1, n2, mat2); 
  
// This code is contributed by ishankhandelwals.

Output

3 3 
6 6

Time complexity: O(N³)
Auxiliary Space: O(M1 * N2)

Related Article: Strassen’s Matrix Multiplication

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Last Updated : 16 Feb, 2023