Remove the columns in media library

The hook for these columns is manage_media_columns. So just filter the columns here:

add_filter( 'manage_media_columns', 'wpse_77687_remove_media_columns' );

function wpse_77687_remove_media_columns( $columns )
{
    unset( $columns['author'] );
    unset( $columns['comments'] );
    return $columns;
}