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PHP Program to Check if a Matrix is Symmetric

Last Updated : 23 Jul, 2025
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A square matrix is said to be a symmetric matrix if the transpose of the matrix is the same as the given matrix. A Symmetric matrix can be obtain by changing row to column and column to row.

Examples: 

Input : [ [ 1, 2, 3 ],
               [ 2, 1, 4 ],
               [ 3, 4, 3 ] ]
Output : Yes

Input : [ [ 3, 5, 8 ],
               [ 3, 4, 7 ],
               [ 8, 5, 3 ] ]
Output : No

Simple solution-

  • Create transpose of a given matrix. 
  • Check if transpose and given matrices are same or not.  
PHP 
<?php
// Simple PHP code for check a matrix is
// symmetric or not.

// Returns true if mat[N][N] is
// symmetric, else false
function isSymmetric($mat, $N) {
    $tr = [[]];
    for ($i = 0; $i < $N; $i++) {
        for ($j = 0; $j < $N; $j++) {
            $tr[$i][$j] = $mat[$j][$i];
        };
    }

    // Fills transpose of
    // mat[N][N] in tr[N][N]
    for ($i = 0; $i < $N; $i++) {
        for ($j = 0; $j < $N; $j++) {
            if ($mat[$i][$j] != $tr[$i][$j]) {
                return false;
            }
        };
    }
    return true;
}

// Driver code
$mat = [[1, 3, 5], [3, 2, 4], [5, 4, 1]];

if (isSymmetric($mat, 3)) {
    echo "Yes";
} else {
    echo "No";
}

?>

Output
Yes

Time Complexity: O(N x N) 

Auxiliary Space: O(N x N)

An Efficient solution to check a matrix is symmetric or not is to compare matrix elements without creating a transpose. We basically need to compare mat[i][j] with mat[j][i].  

PHP 
<?php
// Efficient PHP code for 
// check a matrix is
// symmetric or not.

$MAX = 100;

// Returns true if mat[N][N] 
// is symmetric, else false
function isSymmetric($mat, $N) {
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if ($mat[$i][$j] != $mat[$j][$i])
                return false;
    return true;
}

// Driver code
$mat = array(array(1, 3, 5),
             array(3, 2, 4),
             array(5, 4, 1));

if (isSymmetric($mat, 3))
    echo("Yes");
else
    echo("No");

?>

Output
Yes

Time Complexity: O(N x N) 

Auxiliary Space: O(1)

Please refer complete article on Program to check if a matrix is symmetric for more details!


K

kartik
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