  Let H be a Hopf algebra of dimension pq over an algebraically closed field of
characteristic 0, where p <= q are odd primes. Suppose that S is the antipode
of H. If H is not semisimple, then S^{4p}=id_H and Tr(S^{2p}) is an integer
divisible by p^2. In particular, if dim H = p^2, we prove that H is isomorphic
to a Taft algebra. We then complete the classification for the Hopf algebras of
dimension p^2.
