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## Homework Statement

Derive [itex] [L_\pm , L^2]=0 [/itex]

## Homework Equations

[itex] L_{\pm}=L_x \pm iL_y [/itex]

## The Attempt at a Solution

[itex] [L_\pm , L^2]=[L_x,L_x^2] \pm i[L_y,L_y^2]=[L_x,L_x]L_x + L_x[L_x,L_x] \pm i([L_y,L_y]L_y+L_y[L_y,L_y]) [/itex]

Is this right so far? If so, how do I proceed from this? The books and websites I'll read always just state [itex] [L_\pm , L^2]=0 [/itex] instead of proving it.