C++ Program to check idempotent matrix

Given N * N matrix and the task is to check matrix is an idempotent matrix or not.
Idempotent matrix: A matrix is said to be an idempotent matrix if the matrix multiplied by itself returns the same matrix. The matrix M is said to be an idempotent matrix if and only if M * M = M. In an idempotent matrix M is a square matrix.

Examples: 

Input : mat[][] = {{3, -6},
                   {1, -2}};
Output : Idempotent Matrix

Input : mat[N][N] = {{2, -2, -4},
                     {-1, 3, 4},
                     {1, -2, -3}}
Output : Idempotent Matrix.
 

C++

// Program to check given matrix
// is idempotent matrix or not.
#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 idempotent
// property of matrix.
bool checkIdempotent(int mat[][N])
{
    // Calculate multiplication of matrix
    // with itself and store it into res.
    int res[N][N];
    multiply(mat, res);

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

// Driver function.
int main()
{
    int mat[N][N] = {{2, -2, -4},
                    {-1, 3, 4},
                    {1, -2, -3}};

    // checkIdempotent function call.
    if (checkIdempotent(mat))
        cout << "Idempotent Matrix";
    else
        cout << "Not Idempotent Matrix.";
    return 0;
}

Output

Idempotent Matrix

Time Complexity: O(N³)
Auxiliary Space: O(N²)

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