3. (a) Let V be the complex vector space of all 2 x 2 complex matrices, and consider the operator C defined by C A) = OyAoy, where Oy is the second Pauli spin matrix and A is any matrix in the space. Show that C is a linear operator. Find the 4 x 4 matrix representation of C with respect to the basis 1) = 0 0 , 127 = (0 0), 13) -(1 0) ), 14) - (8 9) (Remember that this is a four dimensional vector space, and the matrix representation of these basis vectors is in terms of four dimensional column vectors.) (b) What are the eigenvalues and 2 x 2 matrix eigenvectors of the operator C