Question 6. Matrices
Consider the following 3 x 3 matrix:
$$A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -2 & 1 & 2 \end{pmatrix}.$$
Let I be the 3 x 3 identity matrix.
a) Find the characteristic polynomial $$f(x) = det(xI - A)$$, and verify the Cayley-Hamilton Theorem in this case: $$f(A) = 0$$.
b) Find the minimal polynomial $$p(x)$$ of A.
c) Determine if A is similar to a diagonal matrix, and if so, identify a diagonal matrix that is similar to A.