Program to multiply two matrices

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

Examples:

Input : mat1[][] = {{1, 2}, 
                   {3, 4}}
        mat2[][] = {{1, 1}, 
                    {1, 1}}
Output : {{3, 3}, 
          {7, 7}}
Input : mat1[][] = {{2, 4}, 
                    {3, 4}}
        mat2[][] = {{1, 2}, 
                    {1, 3}}       
Output : {{6, 16}, 
          {7, 18}}



Multiplication of Square Matrices :
The below program multiplies two square matrices of size 4*4, we can change N for different dimension.

C++

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// C++ program to multiply 
// two square matrices.
#include <iostream>
  
using namespace std;
  
#define N 4
  
// This function multiplies 
// mat1[][] and mat2[][], and 
// stores the result in res[][]
void multiply(int mat1[][N], 
              int mat2[][N], 
              int res[][N])
{
    int i, j, k;
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
        {
            res[i][j] = 0;
            for (k = 0; k < N; k++)
                res[i][j] += mat1[i][k] * 
                             mat2[k][j];
        }
    }
}
  
// Driver Code
int main()
{
    int i, j;
    int res[N][N]; // To store result
    int mat1[N][N] = {{1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3},
                      {4, 4, 4, 4}};
  
    int mat2[N][N] = {{1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3},
                      {4, 4, 4, 4}};
  
    multiply(mat1, mat2, res);
  
    cout << "Result matrix is \n";
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
        cout << res[i][j] << " ";
        cout << "\n";
    }
  
    return 0;
}
  
// This code is contributed
// by Soumik Mondal

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C

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// C program to multiply two square matrices.
#include <stdio.h>
#define N 4
  
// This function multiplies mat1[][] and mat2[][],
// and stores the result in res[][]
void multiply(int mat1[][N], int mat2[][N], int res[][N])
{
    int i, j, k;
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
        {
            res[i][j] = 0;
            for (k = 0; k < N; k++)
                res[i][j] += mat1[i][k]*mat2[k][j];
        }
    }
}
  
int main()
{
    int mat1[N][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};
  
    int mat2[N][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};
  
    int res[N][N]; // To store result
    int i, j;
    multiply(mat1, mat2, res);
  
    printf("Result matrix is \n");
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
           printf("%d ", res[i][j]);
        printf("\n");
    }
  
    return 0;
}

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Java

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// Java program to multiply two square
// matrices.
import java.io.*;
  
class GFG {
      
  
    static int N = 4;
      
    // This function multiplies mat1[][]
    // and mat2[][], and stores the result
    // in res[][]
    static void multiply(int mat1[][], 
                  int mat2[][], int res[][])
    {
        int i, j, k;
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < N; j++)
            {
                res[i][j] = 0;
                for (k = 0; k < N; k++)
                    res[i][j] += mat1[i][k] 
                                * mat2[k][j];
            }
        }
    }
  
    // Driver code
    public static void main (String[] args) 
    {
        int mat1[][] = { {1, 1, 1, 1},
                         {2, 2, 2, 2},
                         {3, 3, 3, 3},
                         {4, 4, 4, 4}};
  
        int mat2[][] = { {1, 1, 1, 1},
                         {2, 2, 2, 2},
                         {3, 3, 3, 3},
                         {4, 4, 4, 4}};
  
        // To store result
        int res[][] = new int[N][N] ;
        int i, j;
        multiply(mat1, mat2, res);
      
        System.out.println("Result matrix"
                                + " is ");
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < N; j++)
                System.out.print( res[i][j]
                                    + " ");
            System.out.println();
        }
    }
}
  
// This code is contributed by anuj_67.

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Python 3

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# 4x4 matrix multiplication using Python3
# Function defination
def matrix_multiplication(M,N):
    # List to store matrix multiplication result
    R = [[0, 0, 0, 0], 
        [0, 0, 0, 0], 
        [0, 0, 0, 0],
        [0, 0, 0, 0]] 
  
    for i in range(0, 4): 
        for j in range(0, 4):
            for k in range(0, 4): 
                R[i][j] += M[i][k] * N[k][j] 
  
    for i in range(0,4): 
        for j in range(0,4): 
            #if we use print(), by default cursor moves to next line each time, 
            #Now we can explicitly define ending character or secuence passing
            #second parameter as end="<character or string>"
            #syntax: print(<variable or value to print>, end="<ending with>")
            #Here space (" ") is used to print a gape after printing 
            #each element of R
            print(R[i][j],end=" ")
        print("\n",end="")
  
# First matrix. M is a list
M = [[1, 1, 1, 1], 
    [2, 2, 2, 2], 
    [3, 3, 3, 3],
    [4, 4, 4, 4]]
  
# Second matrix. N is a list
N = [[1, 1, 1, 1], 
    [2, 2, 2, 2], 
    [3, 3, 3, 3],
    [4, 4, 4, 4]] 
      
# Call matrix_multiplication function
matrix_multiplication(M,N)
  
# This code is contributed by Santanu

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C#

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// C# program to multiply two square
// matrices.
using System;
  
class GFG {
      
  
    static int N = 4;
      
    // This function multiplies mat1[][]
    // and mat2[][], and stores the result
    // in res[][]
    static void multiply(int[,] mat1, 
                int [,]mat2, int [,]res)
    {
        int i, j, k;
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < N; j++)
            {
                res[i,j] = 0;
                for (k = 0; k < N; k++)
                    res[i,j] += mat1[i,k] 
                                * mat2[k,j];
            }
        }
    }
  
    // Driver code
    public static void Main () 
    {
        int [,]mat1 = { {1, 1, 1, 1},
                        {2, 2, 2, 2},
                        {3, 3, 3, 3},
                        {4, 4, 4, 4}};
  
        int [,]mat2 = { {1, 1, 1, 1},
                        {2, 2, 2, 2},
                        {3, 3, 3, 3},
                        {4, 4, 4, 4}};
  
        // To store result
        int [,]res = new int[N,N] ;
        int i, j;
        multiply(mat1, mat2, res);
      
        Console.WriteLine("Result matrix"
                                + " is ");
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < N; j++)
                Console.Write( res[i,j]
                                    + " ");
            Console.WriteLine();
        }
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// PHP program to multiply two 
// square matrices.
  
// This function multiplies mat1[][] and 
// mat2[][], and stores the result in res[][]
function multiply(&$mat1, &$mat2, &$res)
{
    $N = 4;
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = 0; $j < $N; $j++)
        {
            $res[$i][$j] = 0;
            for ($k = 0; $k < $N; $k++)
                $res[$i][$j] += $mat1[$i][$k] * 
                                $mat2[$k][$j];
        }
    }
}
  
// Driver Code
$mat1 = array(array(1, 1, 1, 1),
              array(2, 2, 2, 2),
              array(3, 3, 3, 3),
              array(4, 4, 4, 4));
  
$mat2 = array(array(1, 1, 1, 1),
              array(2, 2, 2, 2),
              array(3, 3, 3, 3),
              array(4, 4, 4, 4));
  
multiply($mat1, $mat2, $res);
$N = 4;
echo ("Result matrix is \n");
for ($i = 0; $i < $N; $i++)
{
    for ($j = 0; $j < $N; $j++)
    {
        echo ($res[$i][$j]);
        echo(" ");
    }
    echo ("\n");
}
  
// This code is contributed 
// by Shivi_Aggarwal 
?>

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Output:

Result matrix is
10 10 10 10
20 20 20 20
30 30 30 30
40 40 40 40 

Multiplication of Rectangular Matrices :
We use pointers in C to multiply to matrices. Please refer the following post as a prerequisite of the code.

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

C++

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// 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] = { { 2, 4 }, { 3, 4 } };
    int mat2[][2] = { { 1, 2 }, { 1, 3 } };
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;
    multiply(m1, m2, mat1, n1, n2, mat2);
    return 0;
}
  
// This code is contributed 
// by Akanksha Rai(Abby_akku)

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C

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// 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] = { { 2, 4 }, { 3, 4 } };
    int mat2[][2] = { { 1, 2 }, { 1, 3 } };
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;
    multiply(m1, m2, mat1, n1, n2, mat2);
    return 0;
}

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Output:

6 16
7 18

The time complexity of the above program is O(n3). It can be optimized using Strassen’s Matrix Multiplication

This article is contributed by Aditya Ranjan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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