Show that, for all $\rho > 0$ and all $n \in \mathbb { N } ^ { * }$, the sets $\mathscr { D } _ { \rho } ( \mathbb { R } )$ and $\mathscr { D } _ { \rho } \left( \mathscr { M } _ { n } ( \mathbb { R } ) \right)$ are closed under multiplication.
Show that, for all $\rho > 0$ and all $n \in \mathbb { N } ^ { * }$, the sets $\mathscr { D } _ { \rho } ( \mathbb { R } )$ and $\mathscr { D } _ { \rho } \left( \mathscr { M } _ { n } ( \mathbb { R } ) \right)$ are closed under multiplication.