2- Prove that the Dirac matrices ; and 3 can be always written as diagonal matrices 00... 0 a1 0 [b00 0b0 0 .... a 0 0 ... 0 = and 3= : : : : : : 0 00 ... 000 bN ... aN where (a,) = 1 and (b) = 1, for all v = 1,2,..., N. V 3- If is a Hermitian operator acts on state ), such that |) = a), Prove that the unitary transformation ' such that ' = , satisfies A|) = a), where ) = U), is the state vector rotation.