Quick question about antisymmetric relationship.

Question

Here we go, It is a really yes or no question. If aRb is a|b then is this antisymmetric? a, b belongs to integers including 0*

Answer 1

Is it? Consider if $a \mid b$ and $b \mid a$. Can this happen for integers $a,b$ and them not be equal?

Hint: Consider $b=-a$.

Solution:

Consider $a=1, b=-1$. Each divide the other but $a \ne b$. Therefore no antisymmetry.