Commutation of angular momentum operators

[michbar89]

Homework Statement

None of the operators Lz, Ly and Lx commute. Show that [Lx,Ly] = i(h-cross)Lz

Homework Equations

Where Lx is defined as Lx=-ih ( y delta/delta x - z delta/delta y)
Where Ly is defined as Ly=-ih ( z delta/delta x - x delta/delta z)
Where Lz is defined as Lz=-ih ( x delta/delta y - y delta/delta x)

The Attempt at a Solution

 

[Cyosis]

Use the following commutator identities:

$$\begin{align*} & [A,B+C]=[A,B]+[A,C] \\ & [A,BC]=[A,B]C+B[A,C] \end{align*}$$