# Trace proof

## Homework Statement

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.

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