change attachment custom field onChange event

Replace the function into your functions.php file –

function update_dynamic_select() { 

 update_post_meta($_POST['aid'], $_POST['field'], $_POST['value']);

echo  $_POST['value'];

die();
}

Replace options in your HTML part –

<?php
$val = get_post_meta( 104, '_image_matmenys', true );

$s1 = ($val == "10x10") ? 'selected="selected"' : '';

$s2 = ($val == "20x20") ? 'selected="selected"' : '';

$s3 = ($val == "30x30") ? 'selected="selected"' : '';

?>

<option value="10x10" <?php echo $s1;?>>10x10</option>

<option value="20x20" <?php echo $s2;?>>20x20</option>

<option value="30x30" <?php echo $s3;?>>30x30</option>

EDIT:

Also, add one more hook –

add_action( 'wp_ajax_nopriv_dynselect', 'update_dynamic_select' );

and make sure that variable ajaxurl has value admin_url('admin-ajax.php') i.e. var ajaxurl="<?php echo admin_url("admin-ajax.php");?>"