Prove that
(a) [Li, xj] = ih&ijkXk (i, j, k = 1, 2, 3) where L = Lx, L2 = Ly, L3 = L and x = x, x2 = y and x3 = z. The symbol &ijk, called the Levi-Civita antisymmetric symbol, is such that
1, if ijk = 123, 231, 312 &ijk = {-1, if ijk = 321, 213, 132 0. otherwise.
(b) [Li, Pj] = ih&ijkPk where p = px, P2 = Py, P3 = Pz (c) L · r = L · p = 0.