## diagonalizability question

Let V be the space of n X n matrices over F. Let A be a fixed n X n matrix
over F. Let T and U be the linear operators on V defined by
T(B) = AB
U(B) = AB - BA.
(a) True or false? If A is diagonalizable (over F), then T is diagonalizable.
(b) True or false? If A is diagonalizable, then U is diagonalizable
Thanks for the help.