How to check if a given matrix is an idempotent matrix

What is an idempotent matrix?

A matrix is called an idempotent matrix if the matrix when multiplied by itself results in the same matrix, i.e., $x * x = x$ .

The following are some examples of idempotent matrices:

Example 1:

[[0,0],
 [0,0]]

Example 2:

[[2, -2, -4],
 [-1, 3, 4],
 [1, -2, -3]]

import java.util.Arrays;
public class Main {
    private static void printMatrix(int[][] matrix){
        for(int[] row: matrix){
            System.out.println(Arrays.toString(row));
        }
    }
    private static int[][] multiplyMatrix(int numRows1, int numCols1, int[][] matrix1, int numRows2, int numCols2, int[][] matrix2) throws Exception {
        if(numCols1 != numRows2){
            throw new Exception("Invalid dimensions for matrix multiplication");
        }
        int[][] result = new int[numRows1][numCols2];
        for (int i = 0; i < numRows1; i++) {
            for (int j = 0; j < numCols2; j++) {
                for (int k = 0; k < numRows2; k++)
                    result[i][j] += matrix1[i][k] * matrix2[k][j];
            }
        }
        return result;
    }
    private static boolean checkIdempotentMatrix(int[][] matrix) throws Exception {
        int[][] result = multiplyMatrix(matrix.length, matrix[0].length, matrix, matrix.length, matrix[0].length, matrix);
        if(result.length != matrix.length || result[0].length != matrix[0].length) return false;
        for(int i=0;i < matrix.length; i++){
            for (int j = 0; j < matrix[i].length; j++)
                if(result[i][j] != matrix[i][j]) return false;
        }
        return true;
    }
    private static void wrapper(int[][] matrix) throws Exception {
        printMatrix(matrix);
        if(checkIdempotentMatrix(matrix)) System.out.println("The matrix is a idempotent matrix");
        else System.out.println("The matrix is not a idempotent matrix");
    }
    public static void main(String[] args) throws Exception {
        int[][] matrix = {{0, 0},{0,0}};
        wrapper(matrix);
        System.out.println("-------------");
        int[][] matrix1 = {{4, 0},{5, -4}};
        wrapper(matrix1);
    }
}

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How to check if a given matrix is an idempotent matrix

What is an idempotent matrix?

Algorithm

Code