Some rank equalities of some outer inverses of the same matrix

By using the properties of outer inverses of matrix and the necessary and sufficient condition of the solution of the matrix equation MFX+YEM=N,the ranks of some outer inverses of the same matrix A is researched and some rank equalities of outer inverses of the matrix A is obtained,which generalized the results of Tian Y and Styan G P H(when does rank(ABC)=rank(AB)+rank(BC)-rank(B)hold?Internat J Math ED Sci.Technol,2002,33:127～137.).