For each of the following matrices A ∈ Mnxn (R), test A for diagonalizability, and if A is diagonalizable, find an invertible matrix Q and a diagonal matrix D such that Q⁻¹ AQ = D.
(a) (1 2)
(0 1)
(b) (1 3)
(3 1)
(c) (1 4)
(3 2)
(d) (7 -4 0)
(8 -5 0)
(6 -6 3)
(e) (0 0 1)
(1 0 -1)
(0 1 1)
(f) (1 1 0)
(0 1 2)
(0 0 3)