Show that the trace functional on n X n matrices is unique in the following
sense. If W is the space of n X n matrices over the field F and if f is a linear functional
on W such that f(AB) = f(BA) for each A and B in W, then f is a scalar
multiple of the trace function. If, in addition, f(I) = n, then f is the trace function.
The Attempt at a Solution
I'm not sure how to start with this proof. Any help would be appreciated.