3. Let F be a field such as R or C and Fn×n be the set of all n × n matrices with entries chosen from F. Let A ∈ F, the trace of A, denoted by is defined as the sum of all of its diagonal entries, i.e., tr(A) = Xaii. We
i=1
know that Fn×n is a vector space over F. Prove that {A ∈ Fn×n|tr(A) = 0} is a subspace of Fn×n.
