# Eigenvalue Problem

I'm given three matrices: $M_1$, $M_2$ and $M_3$, satisfying commutation relations (Einstein summation)
$[M_i,M_j]=i\epsilon_{ijk}M_k$.
Eigenvalues of $M_3$ and their degeneracy is known and I need to find eigenvalues and degeneracies of $M^2\equiv M_1^2+M_2^2+M_3^2$.
I found that $M^2$ and $M_3$ commute, so they have common set of eigenvectors (but there are also degenerate vectors).