Quantum Physics -- Calculating Commutators

[Bmmarsh]

The problem states:
Calculate the commutators [x,Lx], [y,Lx], [z, Lx], [x, Ly], [y, Ly], [z, Ly]. Do you see a pattern that will allow you to state the commutators of x, y, z with Lz?

Unfortunately, the book that is asking this question is very vague and doesn't go into any of the math involved. Any help pointing me in the right direction would be greatly appreciated.

[Followup Question]:
Repeat the calculation with x,... replaced by px,....

Again, any help would be amazing!
Thanks!

[OlderDan]

http://www.physlink.com/Education/AskExperts/ae374.cfm

Apply the operators to their known eigenfunctions. Are the eigenfunctions of one operator also eigenfunctions of the other?

[Bmmarsh]

Thanks for your help!
From what you said, I assume that the commutators [x, Lx], [z, Lz], and [y, Ly] should be zero. I'll have to go to my TA to get help with the eigenfunctions of the angular momentum. I missed a week of classes, so I'm just trying to catch up =)

Thanks again.