## Elementary Linear Algebra 7th Edition

$W$ 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 $M_{n,n}$.