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