Let $u = (u_k)_{k \geqslant 0}$ be a sequence of $\mathbb{C}$ such that $\mathbb{M}_n(u) \neq \emptyset$. Let $A \in \mathbb{M}_n(u)$. Show that the roots of $\varphi_A$ in $\mathbb{C}$ are exactly the eigenvalues of $A$.
Let $u = (u_k)_{k \geqslant 0}$ be a sequence of $\mathbb{C}$ such that $\mathbb{M}_n(u) \neq \emptyset$. Let $A \in \mathbb{M}_n(u)$. Show that the roots of $\varphi_A$ in $\mathbb{C}$ are exactly the eigenvalues of $A$.