Let A be a real 2 x 2 matrix with a complex eigenvalue = a -

Let A be a real 2 x 2 matrix with a complex eigenvalue λ = a - bi (b ≠ 0) and an associated eigenvector v in C2.
a. Show that A(Re v) = a Rev + b Im v and A(Im v) = - b Rev + a Im v.
b. Verify that if P and C are given as in Theorem 9, then AP = PC.