1. The problem statement, all variables and given/known data 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. 1. True or false? If A is diagonalizable (over F), then T is diagonalizable. 2. True or false? If A is diagonalizable, then U is diagonalizable Thanks for the help. 3. The attempt at a solution I'm guessing that 1 is true and 2 is false. I'm not sure, since these are linear operators rather than simple matrices.