We have to prove some of the basic properties of operations in vector spaces, and sometimes it's easy to make assumptions when doing them, so I just want to make sure I'm correct.
Let V be a vector over a field F
Prove
Begin with
Add the additive inverse
to both sides
Manipulating the L.H.S.
Employing associativity and commutativity
So
Add additive inverse to both sides again and desired result is obtained.
Is this correct?