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 multiply by itself return 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

Implementation:

C++

// Program to implement involutory matrix.
#include <bits/stdc++.h>
#define N 3
using namespace std;

// Function for matrix multiplication.
void multiply(int mat[][N], int res[][N])
{
    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.
bool InvolutoryMatrix(int mat[N][N])
{
    int res[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.
int main()
{
    int mat[N][N] = { { 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))
        cout << "Involutory Matrix";
    else
        cout << "Not Involutory Matrix";

    return 0;
}

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

Python3

# Program to implement involutory matrix.
N = 3;

# Function for matrix multiplication.
def multiply(mat, res):

    for i in range(N):
        for j in range(N):
            res[i][j] = 0;
            for k in range(N):
                res[i][j] += mat[i][k] * mat[k][j];
    return res;

# Function to check involutory matrix.
def InvolutoryMatrix(mat):

    res=[[0 for i in range(N)]
            for j in range(N)];

    # multiply function call.
    res = multiply(mat, res);

    for i in range(N):
        for j in range(N):
            if (i == j and res[i][j] != 1):
                return False;
            if (i != j and res[i][j] != 0):
                return False;
    return True;

# Driver Code
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)):
    print("Involutory Matrix");
else:
    print("Not Involutory Matrix");

# This code is contributed by mits

C#

// C# Program to implement
// involutory matrix.
using System;

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 bool 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 ()
    {

        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))
            Console.WriteLine( "Involutory Matrix");
        else
            Console.WriteLine( "Not Involutory Matrix");


    }
}

// This code is contributed by vt_m

PHP

<?php
// Program to implement
// involutory matrix.

$N = 3;

// Function for matrix
// multiplication.
function multiply($mat, $res)
{
    global $N;
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = 0; $j < $N; $j++)
        {
            $res[$i][$j] = 0;
            for ($k = 0; $k < $N; $k++)
                $res[$i][$j] += $mat[$i][$k] *
                                $mat[$k][$j];
        }
    }
    return $res;
}

// Function to check
// involutory matrix.
function InvolutoryMatrix($mat)
{
    global $N;
    $res;
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            $res[$i][$j] = 0;

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

    for ($i = 0; $i < $N; $i++)
    {
        for ($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 Code
$mat = array(array(1, 0, 0),
             array(0, -1, 0),
             array(0, 0, -1));

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

// This code is contributed by mits
?>

Javascript

<script>

// Javascript to implement involutory matrix.
var N = 3;

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

// Function to check involutory matrix.
function InvolutoryMatrix(mat)
{
    var res = Array(N).fill(0).map(
        x => Array(N).fill(0));

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

    for(var i = 0; i < N; i++)
    {
        for(var 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 code
var 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))
    document.write("Involutory Matrix");
else
    document.write("Not Involutory Matrix");

// This code is contributed by 29AjayKumar

</script>

Output

Involutory Matrix

Time Complexity: O(n³)
Auxiliary Space: O(n²), since n2 extra space has been taken.