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
Add the additive inverse
to both sides
Manipulating the L.H.S.
Employing associativity and commutativity
Add additive inverse to both sides again and desired result is obtained.
Is this correct?