solve this matrixes and explain them to me

5. Pauli matrices are defined as 01 = (9 1).62 = (9 7).03 = 10 (a) Show that Pauli matrices are Hermitian, i.e. the conjugate transpose are themselves. (5 points) (b) For any matrices A and B, define commutator [A, B] = AB - BA and anti-commutator {A, B} = AB + BA. Show that Pauli matrices satisfy oj, ; = ZieijkOk and (ou, 0; } = 28;; 12x2 where i, j, k E {1,2,3} and 12*2 is 2*2 identity matrix. (10 points) (c) Show that for any matrices A, B and C, [A, BC] = [A, B]C + B[A, C] = {A, B}C - B{A, C} (5 points) (d) Prove the Jacobi identity [ A, [B, C]] + [B, [C, A]] + [C, [A, B]] = 0 (5 points)