The commutator of two operators A, B is defined as [A, B] = AB - BA. Prove the following relations which involve commutators of operators A, B, C : [A, B] = a[A, B] a C [a, b] = 0 a EC [A, B+C] = [A, B] + [A, C] [A, BC] = [A, B]C + B[A, C] [[A, B], C]+[[B, C), A] + [[C, A], B] = 0