Math Help - antisymmetric

R = {(a,b) is an element of A cross B with (b,a) an element of R inverse}

Proof:
If R is antisymmetric, then R inverse is antisymmetric

-if you can not prove this I must show a counterexample thanks

You need to show if R is antisymettric, meaning if a<=b and b<=a implies a=b. Then has the same property. It should be clear how to do this by definition.

If
But we know that is antisymmetric so .