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## Homework Statement

Calculate the eigenvalues of the [itex]L_x^2[/itex] matrix.

Calculate the eigenvalues of the [itex]L_z^2[/itex] matrix.

Compare these and comment on the result.

## Homework Equations

[itex]L_x=\frac{1}{2}(L_+ + L_- )[/itex]

## The Attempt at a Solution

I have derived eigenvalues for each: [itex]0[/itex] and [itex]\hbar^2[/itex] for both [itex]L_x^2[/itex] and [itex]L_z^2[/itex]. But why are they identical? I'm finding it difficult in qualitatively explaining why the eigenvalues are the same for both.