Easiest way to see if the file is being cached is to append a query string to the <link />
element so that the browser will re-load it.
To do this you can change your stylesheet reference to something like
<link rel="stylesheet" type="text/css" href="/css/stylesheet.css?v=1" />
Note the v=1
part. You can update this each time you make a new version to see if it is indeed being cached.