From what I understand, an equivalence relation is a relation which must be
- reflexive
- symmetric
- transitive
The relation in question is:
- reflexive because the square of a number is always positive
- symmetric as $xy=yx$
- transitive as if $xy>0$ and $yz>0$, then $xy^2z>0$. Divide the last expression by $y^2$, and we find that $xz>0$
Best Answer
$0^2$ is not positive, so the relation is not reflexive.