Show that the determinant of a symplectic matrix equals either 1 or $-1$. Recall: A matrix $M \in \mathcal{M}_{2n}(\mathbb{R})$ is symplectic if and only if $M^{\top} J_{n} M = J_{n}$.
Show that the determinant of a symplectic matrix equals either 1 or $-1$.
Recall: A matrix $M \in \mathcal{M}_{2n}(\mathbb{R})$ is symplectic if and only if $M^{\top} J_{n} M = J_{n}$.