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.