If A = [aij] is an n x n matrix then the trace of A, Tr(A) is defined as the sum of all elements on the main diagonal A, Tr(A) = n SUM i = 1 aij. Prove

Tr(AB) = Tr(BA)

Tr(AT) = Tr(A)

Tr(ATA)>0

I've got some ideas down about this but I'm just not totally sure how to prove these. Thanks!