Use theorem 4.2.1 to determine which of the following are subspaces of mnn. (a) the set of all diagonal n × n matrices. (b) the set of all n × n matrices a such that det(a) = 0. (c) the set of all n × n matrices a such that tr(a) = 0. (d) the set of all symmetric n × n matrices. (e) the set of all n × n matrices a such that at = −a. (f) the set of all n × n matrices a for which ax = 0 has only the trivial solution. (g) the set of all n × n matrices a such that ab = ba for some fixed n × n matrix b