THE RING OF EQUITABLE MATRICES

We consider the set of all equitable matrices of order n for a given partitionof n. We show that this set is a subring of the ring of square matrices of order n.Moreover, we prove that this set is epimorphic to the ring of square matrices of order k,where k is the number of parts in the given partition. In particular, we prove that thesum, the product and the inverse of equitable matrices are also equitable