Prove that the additive inverse of a vector is unique.

20 viewed last edited 4 years ago
Timothy Lee
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.
Vivekanand Vellanki
Looks good to me