Chapter 4.3, Problem 15E

The trace of an $n\times n$ matrix A, denoted $tr(A)$ , is the sum of its diagonal entries; that is,
$tr(A)=a_{11}+a_{22}+\mathrm{...}+a_{nn}$
Show that
(a) $tr(AB)=tr(BA)$
(b) if A is similar to B, then $tr(A)=tr(B)$