Another solution is to copy content.php from twenty eleven to your child theme and add a line to clear the variable that holds the categories, css or code both work.
With the code you could have categories on the categories or archive pages, by saving content.php as content-archive.php and/or content-categories.php
Find:
<?php
/* translators: used between list items, there is a space after the comma */
$categories_list = get_the_category_list( __( ', ', 'twentyeleven' ) );
if ( $categories_list ):
?>
Then add a line to empty the $categories_list
<?php
/* translators: used between list items, there is a space after the comma */
$categories_list = get_the_category_list( __( ', ', 'twentyeleven' ) );
$categories_list = ''; /* Empty the Variable */
if ( $categories_list ):
?>
HTH
David