How to characterize commutativity equalities for Drazin inverses of matrices Yong Ge Tian (2003) Archivum Mathematicum Necessary and sufficient conditions are presented for the commutativity equalities A * A D = A D A * , A † A D = A D A † , A † A A D = A D A A † , A A D A * = A * A D A and so on to hold by using rank equalities of matrices. Some related topics are also examined.