Your $each
is wrong. Check reference
var myDropDownA = $("#myDropDownA");
var myDropDownB = $("#myDropDownB");
$.each(response, function(index,obj)
{
//alert(index + ": " + obj.A);
myDropDownA.append($("<option />").val(obj.A).text(obj.A));
myDropDownB.append($("<option />").val(obj.B).text(obj.B));
});
Working demo: JSfiddle