We assume that the conditions of questions 4 and 5 are satisfied and that $\lambda(0) = 0, \mu(0) = 1$.
7a. Show that $F \in \mathrm{GL}(V)$.
7b. Show that $E$ and $F$ are not of finite order in the group $\mathrm{GL}(V)$.
7c. Calculate the kernel of $H$ and show that $H^r \neq \operatorname{Id}_V$ for $r \geq 1$.