# Java Program to Check Involutory Matrix

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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