In what scenarios would utilizing matrices in PHP be more advantageous compared to traditional multidimensional arrays for data organization and manipulation?

Matrices in PHP can be more advantageous than traditional multidimensional arrays when dealing with mathematical operations such as matrix multiplication, inversion, and determinant calculation. Matrices provide a more structured and efficient way to handle numerical data, making it easier to perform complex calculations.

// Creating a matrix in PHP using arrays
$matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
];

// Accessing elements in the matrix
echo $matrix[1][2]; // Output: 6

// Performing matrix multiplication
function multiplyMatrices($matrix1, $matrix2) {
    // Perform matrix multiplication logic here
}

// Example of matrix multiplication
$matrix1 = [
    [1, 2],
    [3, 4]
];

$matrix2 = [
    [5, 6],
    [7, 8]
];

$result = multiplyMatrices($matrix1, $matrix2);