Multiply Two Matrices in C++

A matrix is a collection of numbers arranged in rows and columns. We can multiply two matrices if the number of columns in the first matrix should be equal to the number of rows in the second matrix. The product matrix has the number of rows the same as the first matrix and the number of columns the same as the second matrix.

In this article, we will learn the multiplication of two matrices in the C++ programming language.

Matrix Multiplication in C++

Example

Input:
mat1[][] = {{1, 2},
                  {3, 4}}
mat2[][] = {{5, 6},
                   {7, 8}}
Multiplication of two matrices:
{{1*5 + 2*7    1*6 + 2*8},
 {3*5 + 4*7    3*6 + 4*8}}
Output:
{{19, 22},
 {43, 50}}

Algorithm to Multiply Two Matrices

• If the original matrices are of size n1 x n2 and m1 x m2, create a resultant matrix of size n1 x m2.
• Three nested loops will be used for the multiplication of the matrices.
• The first two loops are used to iterate over the rows and columns of the result matrix, respectively.
• The innermost loop performs the multiplication of corresponding elements from the current row of the first matrix and the current column of the second matrix.
• Add these products to get the element of the result matrix.
• Repeat these steps for all elements of the result matrix.

C++ Program to Multiply Two Matrices

We use pointers in C++ to multiply matrices. Please refer to the following post as a prerequisite for the code How to pass a 2D array as a parameter in C?

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 3 // 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, 1 }, { 2, 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;
}

Output

Multiplication of given two matrices is:
3    3    3    
6    6    6    

Complexity Analysis

• Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication
• Auxiliary Space: O(m1 * n2)

For more information, refer to the article – Program to multiply two matrices