inverse.cpp

// C++ program to find adjoint and inverse of a matrix 
#include<bits/stdc++.h> 
using namespace std; 
#define N 4 
void getCofactor(int A[N][N], int temp[N][N], int p, int q, int n) 
{ 
    int i = 0, j = 0; 
    for (int row = 0; row < n; row++) 
    { 
        for (int col = 0; col < n; col++) 
        { 
            if (row != p && col != q) 
            { 
                temp[i][j++] = A[row][col]; 
                if (j == n - 1) 
                { 
                    j = 0; 
                    i++; 
                } 
            } 
        } 
    } 
} 
int determinant(int A[N][N], int n) 
{ 
    int D = 0; // Initialize result 
	if (n == 1) 
        return A[0][0]; 
  
    int temp[N][N]; 
    int sign = 1; 
    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); 
        sign = -sign; 
    } 
  
    return D; 
} 
void adjoint(int A[N][N],int adj[N][N]) 
{ 
    if (N == 1) 
    { 
        adj[0][0] = 1; 
        return; 
    } 
    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 = ((i+j)%2==0)? 1: -1; 
            adj[j][i] = (sign)*(determinant(temp, N-1)); 
        } 
    } 
} 
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; 
} 
  

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; 
    } 
} 
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; 
}