# Tell which of the following subsets are subspaces of the vector space of nxn mat

Tell which of the following subsets are subspaces of the vector space of nxn matrices, $$\displaystyle{M}_{{{n}{x}{n}}}$$
a) The set of nxn matrices with a zero determinant.
b) The invertible matrices.
c) The diagonal matrices.
d) Upper triangular matrices.
e) The nxn matrices, all of $$\displaystyle{M}_{{{n}{x}{n}}}$$.

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Jayden-James Duffy
Subspace of the vector space of nxn matrices, $$\displaystyle{M}_{{{n}{x}{n}}}$$ are the subsets of the diagonal matrices and upper triangular matrices.