Java Program to check idempotent matrix

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

Java

// Java program to check given matrix
// is idempotent matrix or not.
import java.io.*;

class GFG
{
    static int N = 3;

    // Function for matrix multiplication.
    static void multiply(int mat[][], int res[][])
    {
        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.
    static boolean checkIdempotent(int mat[][])
    {
        // Calculate multiplication of matrix
        // with itself and store it into res.
        int res[][] = new int[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 code.
    public static void main (String[] args)
    {
        int mat[][] = {{2, -2, -4},
                       {-1, 3, 4},
                       {1, -2, -3}};

        // checkIdempotent function call.
        if (checkIdempotent(mat))
            System.out.println( "Idempotent Matrix");
        else
            System.out.println("Not Idempotent Matrix.");

    }
}

// This code is contributed by vt_m.

Output:

Idempotent Matrix

Time complexity: O(N³)

Auxiliary space: O(N²)

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