Saving a multiple select in database

I’m trying to save a multiple select of categories in the database for a plugin.
I’m using this Code to display the multiple select:

$categories_list = wp_dropdown_categories( array( 'echo' => 0 ) );
 $categories_list = str_replace( "name='cat' id=", "name='optionName[]' multiple='multiple' style=\"width:100%\" id=", $categories_list );
 echo $categories_list;

And this code for saving

$nabanner_placement_CONTENT_ROLLOVER_new = sanitize_text_field( $_POST['nabanner_placement_CONTENT_ROLLOVER'] );
if (preg_match('/(.*)/', $nabanner_placement_CONTENT_ROLLOVER_new)) {
update_option('nabanner_placement_CONTENT_ROLLOVER', $nabanner_placement_CONTENT_ROLLOVER_new);}

But instead of saving the selected values to the database it just saves the string “Array”.