The reverse order laws for {1,2,3} - and {1,2,4} -inverses of a two-matrix product

In this work we study the reverse order laws for {1,2,3}- and {1,2,4}-inverses of a product of two matrices by using the expressions for maximal and minimal ranks of the generalized Schur complement. The necessary and sufficient conditions for B{1,2,3}A{1,2,3}⊆(AB){1,2,3}B{1,2,3}A{1,2,3}⊆(AB){1,2,3} and B{1,2,4}A{1,2,4}⊆(AB){1,2,4}B{1,2,4}A{1,2,4}⊆(AB){1,2,4} are presented.