Multiplicative groups of finitely generated irreducible matrix rings

In famous L. Fuchs' monograph about infinite abelian groups the problem of description of groups of invertible elements of associative rings with unit was formulated. This article contains a part of solution of the problem for any finitely generated matrix rings over the field of rational numbers. The case of irreducible rings over $Q$ is considered in this article. The effective description of multiplicative groups of such rings in terms of generating elements is given.