# C++ Program to multiply two Matrices

One can define matrices in C++ using 2-D arrays.

In this post I will assume, that you are familiar with the concepts of arrays.

In this post I will show you how to write a C++ program that gives the product of two matrices.

The product of two matrices isn’t always defined.
The product of matrices $A$ and $B$: $A\times B$ is defined only when the no. of columns of $A$ is equal to the no. of rows in matrix $B$.

If $A$ is an $m\times p$ matrix, and $B$ is an $p\times n$ matrix, then the product matrix would be a $m\times n$ matrix, $(A\times B)_{ij} = \sum_{k=1}^pA_{ik}B_{kj}$

With the above, information, we can proceed to write a simple program, to multiply two matrices of given sizes.
We would also need to check whether the matrix product is defined or not.

The program is pretty much self-explanatory.

### PROGRAM:

//Matrix Multiply
#include<iostream>
#include<iomanip>
using namespace std;
int main()
{
int m,n,p,q;

a:cout<<"\nEnter the order of the matrix A:\n";
cin>>m;
cin>>n;
cout<<"\nEnter the order of the matrix B:\n";
cin>>q;
cin>>p;
if(n!=q){
cout<<"\nCan't multiply!\nThe number of columns of A should be equal to the number of rows in B.\n\nPlease enter again!\n\n";
goto a;
}
double a[m][n];
double b[n][p];
double prod[m][p];
cout<<"\nEnter the elements of the matrix A row-wise:\n";
for (int i=0;i<m;i++)
for (int j=0;j<n;j++)
cin>>a[i][j];

cout<<"\nEnter the elements of the matrix B row-wise:\n";
for (int i=0;i<n;i++)
for (int j=0;j<p;j++)
cin>>b[i][j];

for (int i=0;i<m;i++){
for (int j=0;j<p;j++){
prod[i][j]=0;
for(int k=0;k<n;k++){
prod[i][j]=prod[i][j]+a[i][k]*b[k][j];
}
}
}
cout<<"\nThe product AxB is:\n";
for (int i=0;i<m;i++){
for (int j=0;j<p;j++){
cout<<prod[i][j]<<setw(16);
}
cout<<"\n";
}
return 0;
}