Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 34

$W$ is not closed under addition and hence it is not a vector subspace of $M_{n,n}$.

The set $W$ of all $n \times n$ invertible matrices is not a vector subspace of $M_{n,n}$. Indeed; the sum of two invertible matrices not necessarily invertible. So $W$ is not closed under addition and hence it is not a vector subspace of $M_{n,n}$.