If you want to deactivate Premiere Elements 9.0 from your computer, in an opened project go to Help Menu/Deactivate. Deactivate is not the same as uninstall. So if you want to remove Premiere Elements 9.0/9.0.1 from your computer, then do the uninstall the usual Control Panel way.
It has been my experience that if you are doing your uninstalling reinstalling of the same program all on the same computer, you should not need to deactivate the purchased activated serial number. You can if you want to.
If any questions or need clarification, please do not hesitate to ask. Proceed with what you feel comfortable with.