Trace of matrix

For an n x n matrix A, the sum of the diagonal elements is called the trace:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec08/Crazymat1.jpg


(a) Show that trace (AB) = trace (BA) where B is another n x n matrix.
(b) Deduce that: if A is similar to B, then trace (A) = trace (B)
In particular, if A is similar to diag (λ1, λ2, ..., λn), then

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec08/Crazymat2.jpg