Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 33

The set $W$ of all $n \times n$ singular matrices is a vector subspace of $M_{n,n}$.

Since the sum of two singular matrices is a singular matrix and multiplying a singular matrix by a constant is singular, then the set $W$ of all $n \times n$ singular matrices is a vector subspace of $M_{n,n}$.