Let M(n,F) be a vector space of matrices of order n by n.
if there exists aij belongs to F for all i,j belongs to [n],
for all M=(mij), define a linear map f(M)=sum(aij*mij)
i,j are in [n].
if f(MN)=f(NM) and f takes the value n on identity matrix,
then f is trace linear function which is unique.prove this.