According to the theorem of Isaacs, the outer automorphism group of the matrix algebra $ M_{n}(R) $ , where $ R $ is a unique factorization domain, is trivial for every $ n\in{} $ .We study generalizations of this theorem.It is proved that the outer automorphism group of the matrix algebra over an arbitrary highest common factor domain is trivial.For the algebra of formal matrices $ {𝕄}_{n}(R;s) $ over a unique factorization domain $ R $ , the outer automorphism group is determined.As a consequence, we obtain a criterion for the isomorphism between the algebra $ {𝕄}_{n}(R;s) $ and the algebra of formal matrices of order $ n $ with entries in $ R $ .
