Exercise 17

Let $p(x)$ be the polynomial $c_{n}x^{n}+\cdots+c_{1}x+c_{0}$. Show that if $T$ is similar to $S$ then $p(T)=c_{n}T^{n}+\cdots+c_{1}T+c_{0}I$ is similar to $p(S)=c_{n}S^{n}+\cdots+c_{1}S+c_{0}I$.