On automorphism groups of matrices

In this paper we consider the groups of the left (right) automorphisms of matrices and their automorphism groups. Without loss of generality one can take square matrices over the ring of integers. For such a matrix, we suggest the notion of a quasiautomorphism and the correspondent notion of its quasiautomorphism group. The description of doubly transitive groups of the left (right) automorphisms is given with the help of the block designs. The knowledge of the structure of the balanced block designs is used for the calculation of the left (right) automorphisms and the quasiautomorphism groups of circulants. The problem that is under consideration is closely connected with the description of the graph automorphisms, the graph isomorphism problem, and also with the group classification of Boolean functions.