# Commutation of squared angular momentum operators

Hello there. I am trying to proove in a general way that

[Lx2,Lz2]=[Ly2,Lz2]=[Lz2,Lx2]

But I am a little bit stuck. I've tried to apply the commutator algebra but I'm not geting very far, and by any means near of a general proof. Any help would be greatly appreciated.

Thank you.

kith
Hint: $L^2 = L_x^2 + L_y^2 + L_z^2$

Of course! We can show ## [L^2,L_i^2]=0 ## for ## i \in \{x,y,z\} ##

so

## [L_x^2,L_i^2]+[L_y^2,L_i^2]+[L_z^2,L_i^2]=0 ##, and for ## i=z ## and ## i=x## we have the equalities.

Thank you very much for the hint, I should have seen that sooner