1) For any vector v, use v to denote the additive inverse of v. (Note that for this notation to make sense, we must assume that v has a unique additive inverse.) Then give a good proof (citing the axioms) that for all v V, (v) = v.

2)Give a good proof of the following, starting from the axioms of a vector space: For all v V , there exists a unique w V such that v + w = 0 (You may assume what we proved in class, that 0 is unique, but do not use the previous problem.)