Chapter 9.8, Problem 1E

In Problems 1-6, (a) show that the given matrix A satisfies ${\left(A-rI\right)}^k=0$ for some r and some positive integer k and (b) use this fact to determine the matrix $e^{At}$. [Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem.]

$A=\left[\begin{array}{cc}3& -2\\ 0& 3\end{array}\right]$