Prove that the additive inverse of a vector is unique
Suppose is a vector space over a field . Prove that the additive inverse of a vector is unique.
A hint provided for the question is as follows:
Suppose are additive inverses of . Prove that using the axioms of a vector space.
My work so far (uses the hint):
Suppose such that are inverses of .
I'm pretty sure that my current answer is lacking substance, so I could use a hand in making it more solid.
The main issue I'm having is some of the wording. I feel as though there's something I could be missing in the question. The part on "axioms of a vector space" is one I don't entirely understand.