#### Prove that the additive inverse of a vector is unique.

Timothy Lee

0

I'd like to ask if this proof is okay.
----- BEGIN PROOF ------
For all x in some vector space V, there exists some y s.t. x+y=0.
Suppose there also exists a z s.t. x+z = 0.
Then x+y=0=x+z
(x+y)+y=(x+z)+y (x+y)+y=(x+y)+z, using commutativity and associativity of addition.
0+y=0+z
y=z
Therefore, y is unique.
---- END PROOF ----
I'm self studying a more advanced linear algebra book to prepare for next year, and want to make sure I'm on the right path, since I have nobody to ask for help or correct me.