Problem 2. (2 pts) Prove the Pauli matrix identity da dys = 26a8dBy - da878, (1) where o = (0,0%,0) is the vector of Pauli matrices, and a, 3, 7,6 indexes their components. Problem 3. (2 pts) From the above Eq. 1 or otherwise, show that 4S, S,= -2aaasaja-aaaasaj, == a a (2) where Siasaaasais is the spin operator expressed in terms of fermionic creation/annihilation operators, and i j are lattice site indices.