When is B− A− a generalized inverse of AB?

Reverse order law for the Moore–Penrose inverse

“…Then, in [6], the reverse order law for the Moore-Penrose inverse is obtained as a consequence of some set equalities. The reader can find some interesting and related results in [1,5,8,11,[14][15][16][17][18]. In particular, the paper [15] is related to our investigations.…”

Reverse order law for least squares g-inverses of multiple matrix products

“…Greville [1] first gave a necessary and sufficient condition for the reverse order law ðABÞ y ¼ B y A y . Since then, the reverse order law of the g-inverses and reflexive g-inverses of two matrices or multiple matrices has been widely discussed, see [2,[4][5][6][7][8] for the detailed descriptions.…”

An invariance property related to the mixed-type reverse order laws

“…They have attracted considerable attention since the middle 1960s, [11] and recently many interesting results have been obtained, see, eg. [4,[12][13][14][15][16][17][18][19][20]. Let A ∈ C m×n and B ∈ C n× p , a solution to the reverse order law B{1}A{1} ⊆ (AB){1} is recalled in the following.…”