Determination of a matrix by its subclasses of generalized inverses

Abstract

The main result of the paper is: AB+A=A and BA+B=B ⇒ A=B where A+ and B+ are the unique Moore-Penrose inverses of A and B respectively. This is a stronger result than uniqueness of Moore-Penrose inverse. Some other results are established generalizing the earlier result of Rao and Mitra (1971) that a matrix is uniquely determined by the entire class of its g-inverses