A simple question about Haar measure

Question

$G$ is a locally compact Hausdorff topological (multiplicative) group, $m$ is a (left) Haar measure on $G$.

I have known that for any $g\in{G}$, $m(gB)=m(B)$.

My question is, for any Borel measurable set $B$, $m(B)>0$, can we conclude that $m(B^{-1})>0$, too?

is this always right? Is there any counterexample?

Thanks a lot.