We denote by $\operatorname { OSp } _ { n } ( \mathbb { R } ) = \operatorname { Sp } _ { n } ( \mathbb { R } ) \cap \mathrm { O } _ { n } ( \mathbb { R } )$ the set of real symplectic and orthogonal matrices, and $\mathcal { C } _ { J } = \left\{ M \in \mathcal { M } _ { n } ( \mathbb { R } ) \mid J M = M J \right\}$ the centralizer of $J$. Show that $\operatorname { OSp } _ { n } ( \mathbb { R } ) \subset \mathcal { C } _ { J }$.