# Matrix multiplication algorithm

In this section we will see how to multiply two matrices. The matrix multiplication can only be performed, if it satisfies this condition. Suppose two matrices are A and B, and their dimensions are A (m x n) and B (p x q) the resultant matrix can be found if and only if n = p. Then the order of the resultant matrix C will be (m x q).

## Algorithm

matrixMultiply(A, B):
Assume dimension of A is (m x n), dimension of B is (p x q)
Begin
if n is not same as p, then exit
otherwise define C matrix as (m x q)
for i in range 0 to m - 1, do
for j in range 0 to q – 1, do
for k in range 0 to p, do
C[i, j] = C[i, j] + (A[i, k] * A[k, j])
done
done
done
End

## Example

Live Demo

#include<iostream>
using namespace std;
int main() {
int product[10][10], r1=3, c1=3, r2=3, c2=3, i, j, k;
int a[3][3] = {
{2, 4, 1},
{2, 3, 9},
{3, 1, 8}
};
int b[3][3] = {
{1, 2, 3},
{3, 6, 1},
{2, 4, 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
3 1 8
The second matrix is:
1 2 3
3 6 1
2 4 7
Product of the two matrices is:
16 32 17
29 58 72
22 44 66

Updated on: 27-Aug-2019

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