Please help with the following QM question regarding matrix representations of the operators S.

In class we computed the matrix representations of the operators 355, Sy, and S 2 for spin1/2. In particular, we found that S 2 go, with 0' the Pauli matrices. Now, repeat this exercise for spin 3/2 particles. Take |3/2,3/2) = (1,0,0,0)T, |3/2,1/2) = (0,1,0,0)T, |3/2,71/2) = (0,0,1,0)T, and |3/2, 73/2) = (0,0,0,1)T. Write your answer as S = gag/2 and compute, in particular, the matrices 03/2