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
.
Then
.
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.