C++ Program to check Involutory Matrix

Given a matrix and the task is to check matrix is an involutory matrix or not. 
Involutory Matrix: A matrix is said to be an involutory matrix if matrix multiply by itself returns the identity matrix. The involutory matrix is the matrix that is its own inverse. The matrix A is said to be an involutory matrix if A * A = I. Where I is the identity matrix. 

Examples:

Input : mat[N][N] = {{1, 0, 0},

                     {0, -1, 0},

                     {0, 0, -1}}

Output : Involutory Matrix

Input : mat[N][N] = {{1, 0, 0},

                     {0, 1, 0},

                     {0, 0, 1}} 

Output : Involutory Matrix

C++

// Program to implement involutory matrix.
#include <bits/stdc++.h>
#define N 3
using namespace std;

// Function for matrix multiplication.
void multiply(int mat[][N], int res[][N])
{
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            res[i][j] = 0;
            for (int k = 0; k < N; k++)
                res[i][j] += mat[i][k] * mat[k][j];
        }
    }
}

// Function to check involutory matrix.
bool InvolutoryMatrix(int mat[N][N])
{
    int res[N][N];

    // multiply function call.
    multiply(mat, res);

    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (i == j && res[i][j] != 1)
                return false;
            if (i != j && res[i][j] != 0)
                return false;
        }
    }
    return true;
}

// Driver function.
int main()
{
    int mat[N][N] = { { 1, 0, 0 },
                      { 0, -1, 0 },
                      { 0, 0, -1 } };

    // Function call. If function return
    // true then if part will execute otherwise
    // else part will execute.
    if (InvolutoryMatrix(mat))
        cout << "Involutory Matrix";
    else
        cout << "Not Involutory Matrix";

    return 0;
}

Output :

Involutory Matrix

Time complexity: O(N³)
Auxiliary space: O(N²)

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