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?