# Matrix multiplication algorithm

Data Structure AlgorithmsAnalysis of AlgorithmsAlgorithms

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, r1=3, c1=3, r2=3, c2=3, i, j, k;
int a = {
{2, 4, 1},
{2, 3, 9},
{3, 1, 8}
};
int b = {
{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