What is the commutator [J^hat_x J^hat_y,J^hat_z] equivalent to?

[pinkfishegg]

Homework Statement

Let J-hat be a quantum mechanial angular momentum operator. The commutator [J^hat_x J^hat_y,J^hat_z] is equivalent to which of the following

Homework Equations

[J^hat_x,J^hat_y]=iħJ^hat_z
[J^hat_y,J^hat_z]=iħJ^hat_x
[J^hat_z,J^hat_x]=iħJ^hat_y

[A,B]=[AB-BA]

The Attempt at a Solution

I tried to plug this out using commutator relations
[J^hat_x J^hat_y,J^hat_z]=J^hat_x J*hat_y J^hat_x-J^hat_xJ^hat_x J^hat_y
simplifies to
iħ(j^hat_z-J^hat_x)=0

The answer the got for the practice test is -i=(j^hat_x,J^hat_z)
im not sure how the simplified to get this answer. if i simplified mine i would just get J^hat_z=J^hat_x..

 

[blue_leaf77]

I can't follow your calculation, I do not know either what you actually meant when writing "-i=(j^hat_x,J^hat_z)" as such notation has no existing mathematical meaning, as far as I know.
So, $[J_xJ_y,J_z] = J_xJ_yJ_z - J_zJ_xJ_y$, from this try to add and subtract some term, with which you can pair the two terms already existing in the original commutator to form commutators of the form that you have written in "Relevant equations", for example try to add and subtract $J_xJ_zJ_y$.