Is the Commutator [P², Lx] in Quantum Mechanics Zero?

[gfxroad]

Homework Statement

Calculate the commutative
[P²,L_x]

Homework Equations

P²=P²_x+P²_y+P²_z
[P_y,L_x]=-iħP_z
[P_z,L_x]=iħP_y
[P_x,L_x]=[P_y,L_y]=[P_z,L_z]=0

The Attempt at a Solution

[P²,L_x]=[P²_x+P²_y+P²_z,L_x]
=[P²_x,L_x]+[P²_y,L_x]+[P²_z,L_x]
=P_x[P_x,L_x]+[P_x,L_x]P_x+P_y[P_y,L_x]+[P_y,L_x]P_y+P_z[P_z,L_x]+[P_z,L_x]P_z
=-iħ[P_y+P_y]+iħ[P_z+P_z]
=iħ[P²_z+P²_y]

 

[tman12321]

First off, what is your question? Second off, your commutation relations are wrong. For example, [P2,L1]=-iħP3.

 

[gfxroad]

Thanks, I was edited the given (miss-writing)
The question is written in the first step
Calculate the commutative [P^2,Lx]=?

 

[tman12321]

Yes, but what is the question you have about how to do this? You've fixed the typo, but you haven't applied the changes to your solution.

 

[gfxroad]

Please, I want to clear to me is the attempts is wrong or true.
Its an exercise (5.2) page 325 of Quantum Mechanic 2nd edition of Nouredine Zettili. The following is the link of the book.
https://ia601700.us.archive.org/6/items/QuantumMechanicsConceptsAndApplications2ndEdNouredineZettili/Quantum%20Mechanics%20-%20Concepts%20and%20Applications%20-%202ndEd%20-%20Nouredine%20Zettili.pdf

 

[tman12321]

As I said before, you've fixed the typos in your "Relevant Equations", but you haven't applied these changes to your solution.

 

[gfxroad]

tman12321
I was putted the relevant equation directly at the attempt part in the third step of solution.