Denote by G the group of all automorphisms together with all antiautomorphisms. The above remarks imply, that |G| = 2|\!\operatorname{Aut}(R,\cdot)| if a ring (or rng) is noncommutative and self-opposite. If it is commutative or non-self-opposite, then |G| = |\!\operatorname{Aut}(R,\cdot)|.
