Java Program to Check Idempotent Matrix

In the previous article, we have seen Java Program to Find the Product of Middle Row and Middle Column of a Matrix

In this article we are going to see how we can write a program to check whether matrix is Idempotent Matrix or not.

Java Program to Check Idempotent Matrix

A 3*3 Matrix is having 3 rows and 3 columns where this 3*3 represents the dimension of the matrix. Means there are 3*3 i.e. total 9 elements in a 3*3 Matrix.

Let’s understand it in more simpler way.

                   | A00   A01   A02 |
Matrix A =  | A10   A11   A12 |
                   | A20   A21   A22 | 3*3

Matrix A represents a 3*3 matrix.
‘A‘ represents the matrix element
‘Aij‘ represents the matrix element at it’s matrix position/index.
‘i‘ represents the row index
‘j‘ represents the column index
Means A00=Aij where i=0 and j=0, A01=aij where i=0 and j=1 and like this.
Here we have started row value from 0 and column value from 0.

A matrix whose product of matrix to itself is equal to that matrix is called idempotent matrix .

Let’s see different ways to to check whether matrix is Idempotent Matrix or not.

By Static Initialization of Array Elements
By Dynamic Initialization of Array Elements

Method-1: Java Program to Check Idempotent Matrix By Static Initialization of Array Elements

Approach :

Declare and initialize a matrix.
Calculate the product to itself .
Check the product of the matrix and the original matrix same or not .

Program :

import java.util.*;

public class Main 
{
   public static void main(String args[])
   {
       Scanner s = new Scanner(System.in);
        // Initializing the 3X3 matrix i.e. 2D array
        int mat[][]={{2,-2,-4},{-1,3,4},{1,-2,-3}};
        int res[][]=new int[3][3];;
        for (int i = 0; i < 3; i++) 
        { 
            for (int j = 0; j < 3; j++) 
            { 
                res[i][j] = 0; 
                for (int k = 0; k < 3; k++) 
                     res[i][j] += mat[i][k] * mat[k][j]; 
            } 
        } 
        for(int i = 0; i < 3; i++) 
            for (int j = 0; j < 3; j++)         
                if (mat[i][j] != res[i][j]) 
                    {
                        System.out.print("Entered matrix not an idempotent matrix .");
                        System.exit(0);
                    }
        System.out.println("Entered matrix is an idempotent matrix");
        
   }
}

Output:

Entered matrix is an idempotent matrix

Method-2: Java Program to Check Idempotent Matrix By Dynamic Initialization of Array Elements

Take input of a matrix from user.
Calculate the product to itself .
Check the product of the matrix and the original matrix same or not .

import java.util.*;
public class Main 
{
   public static void main(String args[])
   {
       Scanner s = new Scanner(System.in);
        // Initializing the 3X3 matrix i.e. 2D array
        int mat[][] = new int[3][3];
        int row, col ;
        // Taking matrix input
        System.out.println("\nEnter matrix elements");
        for(row=0;row<3;row++)
            for(col=0;col<3;col++)
                mat[row][col] = s.nextInt();
        int res[][]=new int[3][3];;
        for (int i = 0; i < 3; i++) 
            { 
                for (int j = 0; j < 3; j++) 
                    { 
                        res[i][j] = 0; 
                        for (int k = 0; k < 3; k++) 
                            res[i][j] += mat[i][k] * mat[k][j]; 
                    } 
            } 
        for(int i = 0; i < 3; i++) 
                for (int j = 0; j < 3; j++)         
                    if (mat[i][j] != res[i][j]) 
                        {
                            System.out.print("Entered matrix not an idempotent matrix .");
                            System.exit(0);
                        }
        System.out.println("Entered matrix is an idempotent matrix");
        
   }
}

Output:

Enter matrix elements
2 -2 -4
-1 3 4
1 -2 -3
Entered matrix is an idempotent matrix

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