# C++ Program to Find Inverse of a Graph Matrix

This is a C++ program to Find Inverse of a Graph Matrix. Inverse of a matrix exists only if the matrix is non-singular i.e., determinant should not be 0. Inverse of a matrix can find out in many ways. Here we find out inverse of a graph matrix using adjoint matrix and its determinant. Steps involved in the Example

Begin
function INV() to get the inverse of the matrix:
Call function DET().
Find the inverse of the matrix using the formula;
End.

## Example

#include<bits/stdc++.h>
using namespace std;
#define N 5
void getCfactor(int M[N][N], int t[N][N], int p, int q, int n) {
int i = 0, j = 0;
for (int r= 0; r< n; r++) {
for (int c = 0; c< n; c++) //Copy only those elements which are not in given row r and column c: {
if (r != p && c != q) { t[i][j++] = M[r][c]; //If row is filled increase r index and reset c index
if (j == n - 1) {
j = 0; i++;
}
}
}
}
}
int DET(int M[N][N], int n) //to find determinant {
int D = 0;
if (n == 1)
return M[0][0];
int t[N][N]; //store cofactors
int s = 1; //store sign multiplier //
To Iterate each element of first row
for (int f = 0; f < n; f++) {
//For Getting Cofactor of M[0][f] do getCfactor(M, t, 0, f, n); D += s * M[0][f] * DET(t, n - 1);
s = -s;
}
return D;
}
if (N == 1) {
}
int s = 1,
t[N][N];
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
//To get cofactor of M[i][j]
getCfactor(M, t, i, j, N);
s = ((i+j)%2==0)? 1: -1; //sign of adj[j][i] positive if sum of row and column indexes is even.
adj[j][i] = (s)*(DET(t, N-1)); //Interchange rows and columns to get the transpose of the cofactor matrix
}
}
}
bool INV(int M[N][N], float inv[N][N]) {
int det = DET(M, N);
if (det == 0) {
cout << "can't find its inverse";
return false;
}
for (int i=0; i<N; i++) for (int j=0; j<N; j++) inv[i][j] = adj[i][j]/float(det);
return true;
}
template<class T> void print(T A[N][N]) //print the matrix. {
for (int i=0; i<N; i++) { for (int j=0; j<N; j++) cout << A[i][j] << " "; cout << endl; }
}
int main() {
int M[N][N] = {
{1, 2, 3, 4,-2}, {-5, 6, 7, 8, 4}, {9, 10, -11, 12, 1}, {13, -14, -15, 0, 9}, {20 , -26 , 16 , -17 , 25}
};
float inv[N][N];
cout << "Input matrix is :\n"; print(M);
cout << "\nThe Inverse is :\n"; if (INV(M, inv)) print(inv);
return 0;
}

## Output

Input matrix is :
1 2 3 4 -2
-5 6 7 8 4
9 10 -11 12 1
13 -14 -15 0 9
20 -26 16 -17 25
The Inverse is :
0.0811847 -0.0643008 0.0493814 -0.0247026 0.0237006
-0.126819 -0.0161738 0.0745377 -0.0713976 0.0151639
0.0933664 0.0028245 -0.0111876 -0.0220437 0.0154006
0.143624 0.0582573 -0.0282371 0.0579023 -0.0175466
-0.15893 0.0724272 0.0259728 -0.00100988 0.0150219