Determine whether the commutativity of (V,+) is independent from the remaining vector space axioms.
The Attempt at a Solution
I am having a really hard time with this problem. Off the top of my head I could not think of any way to prove commutativity using the other axioms. On the other hand, I cannot think of any non-abelian groups (V,+) with a map R x V -> V that satisfies all the desired properties.
If someone could get me pointed in the right direction, it would be appreciated.
Edit: I should clarify that the underlying field is R