27. If A is an *m x n* matrix, B is an *m x n* matrix and AB' = 0, and B'A = 0, show that

(1) A'B = 0,

(2) B'A' = 0,

(3) AB' = 0,

(4) BA' = 0,

(5) B'A = 0,

(6) A'B' = 0.