l. Denote by M3 (Q) the ring of 3 x 3 matrices with rational entries, and consider the 3 x 3 matrix [0 1 0 E M3 (Q) 1 2 -1 (a) Verify that the characteristic polynomial of A is 2t 1 I 0 where I is 2A f(A) 0, i.e. As A By the Cayley-Hamilton Theorem, the 3 x 3 identity matrix (and the right side '0' is a 3 x 3 zero matrix), so we have a subring R C M3 (Q) defined by ao, a1, a2 E Q) These are facts that you may assume. (b) show that R is a field, isomorphic to the field E Qlal of Question 1. In fact, show that there is an isomorphism f E R such that f(a) A. (c) Find explicit matrices B,CE R such that f(p) B and f (h) C under the isomorphism of part (b) (d) Verify that your matrices in (c) satisfy AB AC BC A B C