Let $p > 3$ be a prime, let $E/\mathbb{F}_p$ be a supersingular curve, let $N > \sqrt{p}$ be a prime dividing $p + 1$, and let $\mu_N$ denote the multiplicative group of $N$th roots of unity in $\overline{\mathbb{F}_p}$.
(a) Prove that $\mu_N \subseteq \mathbb{F}_{p^2}$
(b) Prove that $\#E(\mathbb{F}_{p^2}) = (p + 1)^2$ and $E[N] \subseteq E(\mathbb{F}_{p^2})$