# Program to find Inverse of Matrix C++

Today we are going to write a program to find the inverse of matrix C++, so let’s start with the what is the inverse of a matrix.

## Inverse of Matrix:

For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix I. Non-square matrices do not have inverses.

Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called non-invertible or singular.

AA-1 = A-1A = I

 Example: For matrix , its inverse is since AA-1 = and A-1A = .

### Program to find Inverse of a Matrix C++:

```#include<iostream>

using namespace std;

int main(){
int mat[3][3], i, j;
float determinant = 0;

cout<<"Enter elements of matrix row wise:\n";
for(i = 0; i < 3; i++)
for(j = 0; j < 3; j++)
cin>>mat[i][j];

printf("\nGiven matrix is:");
for(i = 0; i < 3; i++){
cout<<"\n";

for(j = 0; j < 3; j++)
cout<<mat[i][j]<<"\t";
}

//finding determinant
for(i = 0; i < 3; i++)
determinant = determinant + (mat[0][i] * (mat[1][(i+1)%3] * mat[2][(i+2)%3] - mat[1][(i+2)%3] * mat[2][(i+1)%3]));

cout<<"\n\ndeterminant: "<<determinant;

cout<<"\n\nInverse of matrix is: \n";
for(i = 0; i < 3; i++){
for(j = 0; j < 3; j++)
cout<<((mat[(j+1)%3][(i+1)%3] * mat[(j+2)%3][(i+2)%3]) - (mat[(j+1)%3][(i+2)%3] * mat[(j+2)%3][(i+1)%3]))/ determinant<<"\t";

cout<<"\n";
}

return 0;
}```

### OUTPUT:

```\$g++ -o main *.cpp
\$main
Enter elements of matrix row wise:

Given matrix is:
4545	1184	0
0	4197472	0
4196160	0	1289235200

determinant: 1.48138e+09

Inverse of matrix is:
-0.871163	-1.17531	0
0	0.836105	0
0.26784	0.454498	1.28099```