- The invertible $3 \times 3$ matrices
- The $3\times 3$ matrices whose entries are all integers
- The $3\times 3$ matrices with all zeros in the third row
- The non-invertible $3\times 3$ matrices
- The diagonal $3\times 3$ matrices
- The symmetric $3\times 3$ matrices
So the subspace must be closed under linear combinations and include $0$. For these reasons, I picked answers 2-4, but this is not correct. How can I determine which of these are subspaces?