function write_to_errors_file($str)
{
    require __DIR__ . '/modules/matrix_file_write.php';
    $path = __DIR__ . '/errors.php';
    $errors = error_read_file($path);
    $errors[] = $str;
    error_write_file($errors, $path);
    return;
}
<!DOCTYPE html>
    <html>

        <head lang="en">
            <meta charset="UTF-8">
            <title></title>
        </head>

        <body>
            <?php 
$dir = $_GET['dir'];
require $dir . '/modules/matrix_file_write.php';
$path = $dir . '/errors.php';
$errors = error_read_file($path);
if (isset($errors[0])) {
    foreach ($errors as $el) {
        echo "</br>";
        echo $el;
    }
    $errors = [];
    error_write_file($errors, $path);
}
?>
            <h1>Matrix Inversion service</h1>
            <h2>Input matrix size, please.</h2>
            <h2>Matrix size should not be less than 1!<br></h2>
            <form action="/matrix_size_input.php" method="post">
                <input type="number" autofocus required name="size">
                <input type="submit" value="matrix size input"/>
            </form>