Question

Let A, B be elements of the vector space V. Show that there exists a unique element X of V such that A+X=B

I need the proof for this question

Answer 1

Here is a hint: Vector space V is an addition abellian group.

Answer 2

I'm still not sure how changing the order of addition will help prove that X is a unique element...where does X+A=B help me to prove that?