Chapter 4 - Vector Spaces - 4.3 Subspaces - Problems - Page 273: 11

See below

We can write set $S$ as $S=\{A \in M_n(R)\}$ and $A$ is invertible. We can notice that $n \times n$ matrix $O$ such as $o_{ij}=0$ for all $1 \leq i \leq n$ and $1 \leq j \leq n$ is not in $S$. Thus, $S$ is not a subspace of $M_n(R)$