Premiere elements 9 is a 32 bit software. From Premiere elements 10 onwards there are 2 version 32 bit and 64 bit.
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aggh that is SO annoying - my computer has 16gb of memory FML
Version 9 was written a LONG time ago... if you want 64bit you need the latest version 12
If you have Premiere Elements 10, 11, or 12 installed on Windows 7, 8, or 8.1 64 bit, then Premiere Elements is a 64 bit application.
Premiere Elements 11 and 12 Mac can be run on Mac 64 bit (with 64 bit processor) as 64 bit applications.
With your Premiere Elements 9.0/9.0.1, it is a 32 bit application running in 32 bit compatibility mode of your Windows 7 64 bit.
See System Requirements for the programs for further details.
You can prove all that to yourself by using the Process Explorer Sysinternals and its Image Type Column to verify 32 bit or 64 bit for the process.