Let W be vector subspace of 2*2 matrices over R such that W is spanned by {AB-BA such that A,B are 2*2 matrices over R},then:

1)prove that dim(W)>=3 by verifyind E12,E21,E11-E22 all belong to W.

2)Considering the trace function tr:M2(R)-->R ,prove that dim(W)=3.

3)Let f:M2(R)-->R be a linear map such that f(AB)=f(BA),then prove that f=c.tr,for some c in R.Hence prove that f=tr if and only if f(Id)=2.

any help or suggestions rare appreciated..thank you