TITLE: $F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
QUESTION [8 upvotes]: $F$ is an isomorphism from group $G$ onto group $B$. Prove $F^{-1}$ is an isomorphism from $B$ onto $G$.
I do not know which direction to go in.

REPLY [6 votes]: Since $F$ is an isomorphism of $G$ onto group $B$ we know that $F^{-1}$ is bijective that being said we know its $1-1$ and onto and all you'd have to do is prove that $F^{-1}$ is operation preserving.