The matrix below can be used to desribe the operator corresponding to the x component of angular momentum of a spin-3/2 particle.
(a) Find the eigenvalues and eigenvectors of this matrix. $$ S_x = \left( \begin{array}{cccc} 0 & \sqrt{3}/2 & 0 & 0\\ \sqrt{3}/2 & 0 & 1 & 0\\ 0 & 1 & 0 & \sqrt{3}/2\\ 0 & 0 &\sqrt{3}/2 & 0 \end{array}\right).$$
(b) The matrix corresponding to the z component of the angular momentum is $$ S_z = \left( \begin{array}{cccc} 3/2 & 0 & 0 & 0\\ 0 & 1/2 & 0 & 0\\ 0 & 0 & -1/2 & 0\\ 0 & 0 & 0 & -3/2 \end{array}\right).$$ Find the commutator $[S_x,S_z] = S_x S_z - S_z S_x$.