hi chrisc, yes you can install on 2 PC, using same serial number. If you want to use on third, you need to deactivate Premiere elements and photoshop elements by help>sign-out from one of the 2 activated computers.In short at a time you can run the software on two machines.
aksagarw has answered the essentials of your question. However, I would add that according to the Adobe License Agreement, you should not be using these programs on these two machines at the same time.
Unless aksagarw as Staff has later information than the currently appearing FAQ cited above.