GENERALIZED INVERSES OF MATRICES OVER COMMUTATIVE RINGS

A Rao-regular matrix and the Rao idempotent of a matrix over a commuta tive ring are defined. We prove that a matrix A over a commutative rin g is regular if and only if A is a sum of Rao-regular matrices with mu tually orthogonal Rao idempotents. We find necessary and sufficient co nditions for a matrix to have group inverse over a commutative ring. A lso, we give a method for computing minors of reflexive g-inverse when ever it exists.