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!
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