Determine which of the following are subspaces of Mnn.
a) The set of all diagonal n x n matrices.
b) The set of all n x n matrices A such that det(A) = 0.
c) The set of all n x n matrices A such that tr(A) = 0.
d) The set of all symmetric n x n matrices.
e) The set of all n x n matrices A such that AT = -A.
f) The set of all n x n matrices A for which Ax = 0 has only the trivial solution.
g) The set of all n x n matrices A such that AB = BA for some fixed n x n matrix B.