Check if a Matrix is Involutory or not in Java?

Matrices are nothing but a collection of data elements arranged in a rectangular layout that is two-dimensional. In Java, an array with two dimensions can be considered as a matrix.

Involutory matrix is a square matrix which when multiplied by itself, gives back an identity matrix. Identity matrix is a matrix in which all elements are zero except the diagonals which are one.

Let’s deep dive into this article, to know how it can be done by using Java programming language.

To show you some instances

Instance-1

Suppose we have a matrix
     | 1 0 0 |
A  = | 0 1 0 |
     | 0 0 1 |

A2 = A X A

     | 1 0 0 |   | 1 0 0 |
   = | 0 1 0 | X | 0 1 0 |
     | 0 0 1 |   | 0 0 1 |
 
     | 1 0 0 |
A2 = | 0 1 0 |
     | 0 0 1 |

It is an involutory matrix.

Instance-2

Suppose we have a matrix

Suppose we have a matrix
     | 1 0 0  |
A  = | 0 -1 0 |
     | 0 0 -1 |
A2 = A X A

     | 1 0 0 |    | 1 0 0 |
   = | 0 -1 0 | X | 0 -1 0|
     | 0 0 -1 |   | 0 0 -1|

     | 1 0 0 |
A2 = | 0 1 0 |
     | 0 0 1 |

It is an involutory matrix.

Algorithm

Step 1 − Initialise and declare the matrix

Step 2 − Multiply the matrix with itself and store the resultant

Step 3 − Compare the product matrix with an identity matrix and check if both matrices are the same or not

Step 4 − If both the matrices are the same then the matrix is an involutory matrix

Multiple Approaches

We have provided the solution in different approaches.

• By Using Static Initialization of Matrix

• By Using Dynamic Initialization of Matrix

Let’s see the program along with its output one by one.

Approach-1: By Using Static Initialization of Matrix

In this approach, matrix elements will be initialized in the program. Then as per the algorithm check if the matrix is an involutory matrix or not.

Example

import java.util.Scanner;
public class Main {
   public static void main(String[] args) {
      // Matrix to be checked
      int mat[][] = {{ 1, 0, 0 },{ 0, -1, 0 },{ 0, 0, -1 },};
      // Print results
      if (invoCheck(mat))
         System.out.println("The matrix is an involutory matrix.");
      else
         System.out.println("The matrix is not an involutory matrix.");
   }
   // Matrix multiplication
   static void mul(int mat[][], int prod[][]) {
      for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
            prod[i][j] = 0;
            
           // Resultant product is stored in prod
            for (int k = 0; k < 3; k++) {
               prod[i][j] += mat[i][k] * mat[k][j];
            }
         }
      }
   }
   // Check if the matrix is involutory
   static boolean invoCheck(int mat[][]) {
      // 3X3 Identity Matrix
      int identityMat[][] = { { 1, 0, 0 },{ 0, 1, 0 },{ 0, 0, 1 } };
      int prod[][] = new int[3][3];
      
      // Calls the matrix multiplication
      mul(mat, prod);
      
      // Checks if the product matrix is an identity matrix
      for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
            if (identityMat[i][j] != prod[i][j])
            return false;
         }
      }
      return true;
   }
}

Output

The matrix is an involutory matrix.

Approach-2: By Using Dynamic Initialization of Matrix

In this approach, matrix elements will be taken as user input in the program. Then as per the algorithm check if the matrix is an involutory matrix or not.

Example

import java.util.Scanner;
public class Main {
   public static void main(String[] args) {
      //Matrix to be checked
      int mat[][] = new int[3][3];
      
      //Take matrix as user input
      Scanner sc = new Scanner(System.in);
      System.out.println("Enter matrix elements:-");
      for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
            mat[i][j] = sc.nextInt();
      }}
      // Print results
      if (invoCheck(mat))
         System.out.println("The matrix is an involutory matrix.");
      else
        System.out.println("The matrix is not an involutory matrix.");
   }
   // Matrix multiplication
   static void mul(int mat[][], int prod[][]) {
      for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
            prod[i][j] = 0;
            
            // Resultant product is stored in prod
            for (int k = 0; k < 3; k++) {
               prod[i][j] += mat[i][k] * mat[k][j];
            }
         }
      }
   }
   // Check if the matrix is involutory
   static boolean invoCheck(int mat[][]) {
      // 3X3 Identity Matrix
      int identityMat[][] = { { 1, 0, 0 },{ 0, 1, 0 },{ 0, 0, 1 } };
      int prod[][] = new int[3][3];
      
      // Calls the matrix multiplication
      mul(mat, prod);
      
      // Checks if the product matrix is an identity matrix
      for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
            if (identityMat[i][j] != prod[i][j])
            return false;
         }
      }
      return true;
   }
}

Output

Enter matrix elements:-
1 0 0
0 1 0
0 0 1
The matrix is an involutory matrix

In this article, we explored different approaches to check if the matrix is an involutory matrix or not by using Java programming language.