Hi all, My motivation is understanding some derivations in Quantum Mechanics, but I think my questions are purely algebraic. I have a general question and then a specific one: General Question - when writing the commutator of commuting vector and a scalar operators (for instance angular momentum and some Hamiltonian) - [itex][\vec A,H]=0[/itex] - what is meant by this *exactly*? I see two possible answers: 1. [itex][A_i,H]=0[/itex] for [itex]i=1,2,3[/itex] 2. [itex][A_1+A_2+A_3,H]=0[/itex] in which case we could have [itex][A_i,H]\ne0[/itex] for some [itex]i[/itex] . It seems to me that in the QM context almost always what is meant is the first option but I'm not certain... Specific Question - if [itex]\vec A[/itex] and [itex]\vec B[/itex] commute with [itex]H[/itex], does [itex]\vec A \cdot \vec B[/itex] also necessarily commute? If the answer to the question above is #1, then obviously it does. If the answer is #2 then I guess not? Would greatly appreciate the clarifications. Thanks!