- #1

metder

- 5

- 0

## Homework Statement

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.

## 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.