Exercise 1.2. Let M denote the set of 4-by-4 matrices whose characteristic polynomial is (λ − 1)(λ − 2) (λ − 3)².
(a) Find an A € M such that all of the eigenspaces of A are 1-dimensional.
(b) Find a B € M such that at least one eigenspace of B is 2-dimensional.
(c) Is it true that C € M implies C is invertible?
(d) Is it true that, for any D € M, no positive power of D equals the identity?
