I'm given the following:
Let V be the set of ordered pairs $(x,y)$ of positive real numbers with addition and scalar multiplication defined by
$$(x_1, y_1) + (x_2,y_2) =(x_1x_2,y_1y_2) $$
$$a(x,y) = (x^a,y^a)$$
My question is with the 5th addition axiom given by
A5: For each element v in V, an element -v in V exists such that $-v+v=0 $ and $v + (-v)=0$
I don't really know how to go about verifying this axiom and judging by the questions wording "Show that V is a vector space by verifying all the axioms" I can't get outta this by saying that V isn't a vector space.