For all $e \in E^p$, we consider $\Omega_p(e) : E^p \rightarrow \mathbb{R}$ defined for all $u \in E^p$ by
$$\Omega_p(e)(u) = \det(\operatorname{Gram}(e, u))$$
(a) Show that for all $e \in E^p$, we have $\Omega_p(e) \in \mathcal{A}_p(E, \mathbb{R})$.
(b) Verify that for all $(e, u) \in E^p \times E^p$, we have $\Omega_p(e)(u) = \Omega_p(u)(e)$.
(c) Show that $\Omega_p \in \mathcal{A}_p(E, \mathcal{A}_p(E, \mathbb{R}))$.