(a) Prove Wilson's theorem, that $(p-1) ! \equiv-1(\bmod p)$, where $p$ is prime.

(b) Suppose that $p$ is an odd prime. Express $1^{2} .3^{2} .5^{2} \ldots(p-2)^{2}(\bmod p)$ as a power of $-1$.

[Hint: $k \equiv-(p-k)(\bmod p)$.]