Java Program to check Involutory Matrix

Given a matrix and the task is to check matrix is involutory matrix or not. 

Involutory Matrix:

A matrix is said to be involutory matrix if matrix multiplied by itself returns the identity matrix. Involutory matrix is the matrix that is its own inverse. The matrix A is said to be involutory matrix if A * A = I. Where I is the identity matrix. 

Examples:

Input : mat[N][N] = {{1, 0, 0},
                     {0, -1, 0},
                     {0, 0, -1}}
Output : Involutory Matrix

Input : mat[N][N] = {{1, 0, 0},
                     {0, 1, 0},
                     {0, 0, 1}} 
Output : Involutory Matrix

Java

// Java  Program to implement
// involutory matrix.
import java.io.*;

class GFG {

    static int N = 3;

    // Function for matrix multiplication.
    static void multiply(int mat[][], int res[][])
    {
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                res[i][j] = 0;
                for (int k = 0; k < N; k++)
                    res[i][j] += mat[i][k] * mat[k][j];
            }
        }
    }

    // Function to check involutory matrix.
    static boolean InvolutoryMatrix(int mat[][])
    {
        int res[][] = new int[N][N];

        // multiply function call.
        multiply(mat, res);

        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if (i == j && res[i][j] != 1)
                    return false;
                if (i != j && res[i][j] != 0)
                    return false;
            }
        }
        return true;
    }

    // Driver function.
    public static void main (String[] args)
    {

        int mat[][] = { { 1, 0, 0 },
                        { 0, -1, 0 },
                        { 0, 0, -1 } };

        // Function call. If function return
        // true then if part will execute
        // otherwise else part will execute.
        if (InvolutoryMatrix(mat))
            System.out.println ( "Involutory Matrix");
        else
            System.out.println ( "Not Involutory Matrix");


    }
}

// This code is contributed by vt_m

Output

Involutory Matrix

Time complexity: O(N³)
Auxiliary space: O(N²)

Please refer complete article on Program to check Involutory Matrix for more details!