[jquery] Add and remove attribute with jquery

First you to add a class then remove id

<script type="text/javascript">
$(document).ready(function(){   
 $("#page_navigation1").addClass("page_navigation");        

 $("#add").click(function(){
        $(".page_navigation").attr("id","page_navigation1");
    });     
    $("#remove").click(function(){
        $(".page_navigation").removeAttr("id");
    });     
  });
</script>