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.
Involutory-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

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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
?>

chevron_right



Output :

Involutory Matrix


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Mithun Kumar



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.