PHP で複数の配列からすべての組み合わせを再帰的に生成するにはどうすればよいですか?

$arrayA = array('A1','A2','A3');
$arrayB = array('B1','B2','B3');
$arrayC = array('C1','C2');

[
    ['A1', 'B1', 'C1'],
    ['A1', 'B1', 'C2'],
    ['A1', 'B2', 'C1'],
    ...
]

function combinations($arrays, $i = 0) {
    // If reaching the last array, return the array itself
    if (!isset($arrays[$i])) {
        return array();
    }
    
    // If at the parent array, return the recursive call to the following array
    if ($i == count($arrays) - 1) {
        return $arrays[$i];
    }
    
    // Get combinations from subsequent arrays
    $tmp = combinations($arrays, $i + 1);

    $result = array();

    // Concatenate each array from tmp with each element from $arrays[$i]
    foreach ($arrays[$i] as $v) {
        foreach ($tmp as $t) {
            $result[] = is_array($t) ? 
                array_merge(array($v), $t) :
                array($v, $t);
        }
    }
    
    return $result;
}

print_r(
    combinations(
        array(
            array('A1','A2','A3'), 
            array('B1','B2','B3'), 
            array('C1','C2')
        )
    )
);