// C++ program to find adjoint and inverse of a matrix
#include <bits/stdc++.h>
using namespace std;
#define N 4
// Function to get cofactor of A[p][q] in temp[][]. n is
// current dimension of A[][]
void getCofactor(int A[N][N], int temp[N][N], int p, int q,
int n)
{
int i = 0, j = 0;
// Looping for each element of the matrix
for (int row = 0; row < n; row++) {
for (int col = 0; col < n; col++) {
// Copying into temporary matrix only those
// element which are not in given row and
// column
if (row != p && col != q) {
temp[i][j++] = A[row][col];
// Row is filled, so increase row index and
// reset col index
if (j == n - 1) {
j = 0;
i++;
}
}
}
}
}
/* Recursive function for finding determinant of matrix.
n is current dimension of A[][]. */
int determinant(int A[N][N], int n)
{
int D = 0; // Initialize result
// Base case : if matrix contains single element
if (n == 1)
return A[0][0];
int temp[N][N]; // To store cofactors
int sign = 1; // To store sign multiplier
// Iterate for each element of first row
for (int f = 0; f < n; f++) {
// Getting Cofactor of A[0][f]
getCofactor(A, temp, 0, f, n);
D += sign * A[0][f] * determinant(temp, n - 1);
// terms are to be added with alternate sign
sign = -sign;
}
return D;
}
// Function to get adjoint of A[N][N] in adj[N][N].
void adjoint(int A[N][N], int adj[N][N])
{
if (N == 1) {
adj[0][0] = 1;
return;
}
// temp is used to store cofactors of A[][]
int sign = 1, temp[N][N];
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Get cofactor of A[i][j]
getCofactor(A, temp, i, j, N);
// sign of adj[j][i] positive if sum of row
// and column indexes is even.
sign = ((i + j) % 2 == 0) ? 1 : -1;
// Interchanging rows and columns to get the
// transpose of the cofactor matrix
adj[j][i] = (sign) * (determinant(temp, N - 1));
}
}
}
// Function to calculate and store inverse, returns false if
// matrix is singular
bool inverse(int A[N][N], float inverse[N][N])
{
// Find determinant of A[][]
int det = determinant(A, N);
if (det == 0) {
cout << "Singular matrix, can't find its inverse";
return false;
}
// Find adjoint
int adj[N][N];
adjoint(A, adj);
// Find Inverse using formula "inverse(A) =
// adj(A)/det(A)"
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
inverse[i][j] = adj[i][j] / float(det);
return true;
}
// Generic function to display the matrix. We use it to
// display both adjoin and inverse. adjoin is integer matrix
// and inverse is a float.
template <class T> void display(T A[N][N])
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
cout << A[i][j] << " ";
cout << endl;
}
}
// Driver program
int main()
{
int A[N][N] = { { 5, -2, 2, 7 },
{ 1, 0, 0, 3 },
{ -3, 1, 5, 0 },
{ 3, -1, -9, 4 } };
int adj[N][N]; // To store adjoint of A[][]
float inv[N][N]; // To store inverse of A[][]
cout << "Input matrix is :\n";
display(A);
cout << "\nThe Adjoint is :\n";
adjoint(A, adj);
display(adj);
cout << "\nThe Inverse is :\n";
if (inverse(A, inv))
display(inv);
return 0;
}
