Php 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

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
?>

Output :

Involutory Matrix

Time complexity: O(N³)

Auxiliary space: O(N²)

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