Let $q \in \mathbb { N } ^ { * }$. Show that the set of invertible matrices of $\mathscr { M } _ { q } ( \mathbb { R } )$ is an open set and that the map $M \mapsto M ^ { - 1 }$ is continuous on this open set.
Let $q \in \mathbb { N } ^ { * }$. Show that the set of invertible matrices of $\mathscr { M } _ { q } ( \mathbb { R } )$ is an open set and that the map $M \mapsto M ^ { - 1 }$ is continuous on this open set.