Premiere Elements 9.0/9.0.1 and Premiere Elements 13 are standalone products.
So, you can have both on the same computer, but only open one for your work.
The classical recommendation is to finish a project in the version in which it was created since there
is no guarantee that a project from an earlier version will open in the later version. Probably will, but
no guarantees. And, when you do explore this, do it from a copy of the earlier version project. Once you
take the earlier version project into a later version one, you cannot go back to edit the later version edited
project in the earlier version program.
If you have both versions (9 and 13) on the same computer and you have not moved, deleted, renamed any of the version 9's files/folders,
right click the saved closed Premiere Elements 9.0/9.0.1 project file, select Open With, and then Adobe Premiere Elements 13.
(Your 9.0/9.0.1 saved closed project file should be found in Libraries/Documents/Adobe/Premiere Elements/9.0.)
Please review and consider. If any questions or need clarification, please do not hesitate to let me know.