A note on Rao and Mitra's constrained inverse and Drazin's (b,c) inverse

The aim of this short note is to indicate that Rao and Mitra's constrained matrix inverse AcrCR (introduced in 1972) is a direct precursor of recently introduced Drazin's (b,c) outer generalized inverse. Precisely, if one rewrites definition of AcrCR in purely multiplicative language, then it turns out that two inverses coincide. Recently introduced Mary's inverse along an element and Manjunatha Prasad and Mohana's core-EP inverse are the special cases of Rao and Mitra's constrained inverse.