You don’t understand the Wikipedia definition of multiplication, the commutative property, or what mathematical equivalence and equality are. See “equivalence relation” on Wikipedia for more information. In short: everything that is equal is also equivalent. These equality/equivalence dictionary definitions you trotted out are meaningless in a mathematical context. You could equally argue an answer is wrong because the dictionary says “set” is a collection of things, which by definition allows duplicate items.
The argument that the answer is incorrect because the teacher hadn’t covered commutativity yet is stupid on its face. Do we really want to penalize students for knowing more than the teacher has covered? This incentivizes students to dumb down to the lowest denominator: the pace of the teacher. If the teacher wants to limit what is taught to students, they should do it in a way that doesn’t prevent students from being marked down for giving objectively correct answers.