# C++ Program to Multiply Two Matrix Using Multi-dimensional Arrays

C++ProgrammingServer Side Programming

A matrix is a rectangular array of numbers that is arranged in the form of rows and columns.

An example of a matrix is as follows.

A 3*3 matrix has 3 rows and 3 columns as shown below −

8 6 3
7 1 9
5 1 9

A program that multiplies two matrices using multidimensional arrays is as follows.

## Example

Live Demo

#include<iostream>
using namespace std;
int main() {
int product, r1=2, c1=3, r2=3, c2=3, i, j, k;
int a = { {2, 4, 1} , {2, 3, 9} };
int b = { {1, 2, 3} , {3, 6, 1} , {2, 9, 7} };
if (c1 != r2) {
cout<<"Column of first matrix should be equal to row of second matrix";
} else {
cout<<"The first matrix is:"<<endl;
for(i=0; i<r1; ++i) {
for(j=0; j<c1; ++j)
cout<<a[i][j]<<" ";
cout<<endl;
}
cout<<endl;
cout<<"The second matrix is:"<<endl;
for(i=0; i<r2; ++i) {
for(j=0; j<c2; ++j)
cout<<b[i][j]<<" ";
cout<<endl;
}
cout<<endl;
for(i=0; i<r1; ++i)
for(j=0; j<c2; ++j) {
product[i][j] = 0;
}
for(i=0; i<r1; ++i)
for(j=0; j<c2; ++j)
for(k=0; k<c1; ++k) {
product[i][j]+=a[i][k]*b[k][j];
}
cout<<"Product of the two matrices is:"<<endl;
for(i=0; i<r1; ++i) {
for(j=0; j<c2; ++j)
cout<<product[i][j]<<" ";
cout<<endl;
}
}
return 0;
}

## Output

The first matrix is:
2 4 1
2 3 9

The second matrix is:
1 2 3
3 6 1
2 9 7

Product of the two matrices is:
16 37 17
29 103 72

In the above program, the two matrices a and b are initialized as follows.

int a = { {2, 4, 1} , {2, 3, 9} };
int b = { {1, 2, 3} , {3, 6, 1} , {2, 9, 7} };

If the number of columns in the first matrix are not equal to the number of rows in the second matrix then multiplication cannot be performed. In this case an error message is printed. It is given as follows.

if (c1 != r2) {
cout<<"Column of first matrix should be equal to row of second matrix";
}

Both the matrices a and b are displayed using a nested for loop. This is demonstrated by the following code snippet.

cout<<"The first matrix is:"<<endl;
for(i=0; i<r1; ++i) {
for(j=0; j<c1; ++j)
cout<<a[i][j]<<" ";
cout<<endl;
}
cout<<endl;
cout<<"The second matrix is:"<<endl;
for(i=0; i<r2; ++i) {
for(j=0; j<c2; ++j)
cout<<b[i][j]<<" ";
cout<<endl;
}
cout<<endl;

After this, the product[][] matrix is initialized to 0. Then a nested for loop is used to find the product of the 2 matrices a and b. This is demonstrated in the below code snippet.

for(i=0; i<r1; ++i)
for(j=0; j<c2; ++j) {
product[i][j] = 0;
}
for(i=0; i<r1; ++i)
for(j=0; j<c2; ++j)
for(k=0; k<c1; ++k) {
product[i][j]+=a[i][k]*b[k][j];
}

After the product is obtained, it is printed. This is shown as follows.

cout<<"Product of the two matrices is:"<<endl;
for(i=0; i<r1; ++i) {
for(j=0; j<c2; ++j)
cout<<product[i][j]<<" ";
cout<<endl;
}