Java Program to Check Involutory Matrix

Java Program to Check Involutory Matrix

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In the previous article, we have seen Java Program to Check Idempotent Matrix

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

Java Program to Check Involutory 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.

Note: A matrix whose product of matrix is inverse  to itself is  to that matrix is called Involutory matrix .

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

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

Approach:

  • Declare and initialize a matrix.
  • Calculate the product to itself .
  • Check the product of the matrix is inverse to the entered matrix 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[][]={{1,0,0},{0,1,0},{0,0,1}};
        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 (i == j && res[i][j] != 1) 
                    {
                        System.out.println("Not a Involutory Matrix"); 
                        System.exit(0);  
                    }
                if (i != j && res[i][j] != 0) 
                    {
                        System.out.println("Not a Involutory Matrix"); 
                        System.exit(0);  
                    }
            } 
        } 
        System.out.println("Involutory Matrix"); 
    } 
}

Output:

Involutory Matrix

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

Approach:

  • Take user input of a matrix.
  • Calculate the product to itself .
  • Check the product of the matrix is inverse to the entered matrix 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[][] = new int[3][3];
        int row, col ;
        // Taking matrix input
        System.out.println("Enter 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 (i == j && res[i][j] != 1) 
                    {
                        System.out.println("Not a Involutory Matrix"); 
                        System.exit(0);  
                    }
                if (i != j && res[i][j] != 0) 
                    {
                        System.out.println("Not a Involutory Matrix"); 
                        System.exit(0);  
                    }
            } 
        } 
        System.out.println("Involutory Matrix"); 
    } 
}

Output:

Enter matrix elements

1 0 0
0 1 0
0 0 1
Involutory Matrix

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