Welcome to the forum.
If you wish to Delete PrE 9, I would go to Control Panel, and Add/Remove Programs (Windows), then choose PrE 9 from the drop-down list of installed programs. When done, I would run a good Registry cleaner, such as CCleaner.
Note: if you have any unfinished PrE 9 Projects, I would first complete those in PrE 9. While they might Open in PrE 11, there might be some issues, as PrE 11 had some significant changes. Also, any Projects on your computer, will not be affected by the Uninstall of PrE 9, so if they are all complete, there will be some more "housecleaning" required.
I don't know about Mac, but in Windows it is VERY BAD to just delete a program folder, since you are leaving behind all the System Registry index entries, which can cause SERIOUS problems for Windows... so do what Hunt said
If you want more information about Windows, search http://search.microsoft.com/search.aspx?mkt=en-US&setlang=en-US
On what computer operating system is your Premiere Elements 9.0/9.0.1 running, some version of Windows or Mac?
If you are running on some version of Windows, then you want to open a new project in Premiere Elements 9.0/9.0.1 and then go to Help Menu/Deactivate. Then close the program, go to Control Panel/Installed Programs and uninstall Premiere Elements 9 there.
After the uninstall, run the ccleaner (regular cleaning and registry cleaning parts) to get rid of any leftovers from incomplete uninstalls/reinstalls.
If you have installed Premiere Elements 9 Content, then check Control Panel/Installed Programs to make sure that Premiere Elements 9 Templates or Content (whatever it is named as) was uninstalled with the program. If not, uninstall that Content in Control Panel area.
Depending on your results with version 11, you may want to keep version 9.0/9.0.1 installed until you feel comfortable with version 11. Just run one program at a time...and provided that your computer is not in a resource crunch.
For Mac counterpart, we will have to wait for the Premiere Elements Mac users for their input. Premiere Elements Windows only user here.