Let $\mathcal{U}_q$ be the set of endomorphisms $\phi \in \mathcal{L}(V)$ that are compatible with $P_a$. Show that $E \in \mathcal{U}_q$ and $F \in \mathcal{U}_q$.
Let $\mathcal{U}_q$ be the set of endomorphisms $\phi \in \mathcal{L}(V)$ that are compatible with $P_a$. Show that $E \in \mathcal{U}_q$ and $F \in \mathcal{U}_q$.