Abstract
In this paper, we provide a classification of automorphisms and involutions of the first kind of the formal matrix algebra \(K_{s}(R)\) over a UFD. We give necessary and sufficient conditions for any given automorphism to be inner. We describe a family of cosets of the subgroup of inner automorphisms in the group of all automorphisms and the outer automorphism group. This allows us to provide an explicit description of involutions. As it appears, for any idempotent \(e\not=E_{11},E_{22}\) there is no more than one involution which sends \(E_{11}\) to \(e\) . We also provide some results on equivalency of involutions.
