The reverse order law for the generalized inverse A(2)T,S

By using the ranks of matrices, the necessary and sufficient condition is given for the reverse order law of the generalized inverse A^(^2^)"T","S of matrix product A=A"1A"2...A"n to hold. As the special cases, similar results for Moore-Penrose inverse A^@?, the weighted Moore-Penrose inverse A^@?"M","N, Drazin inverse A"d and group inverse A"g are also derived.