16. Let $a^{-1}$ be the inverse of $a$ modulo $m$. Prove:
(i) $a n \equiv c(\bmod m)$ holds if and only if $n \equiv a^{-1} c(\bmod m)$.
(ii) $a^{-1} b^{-1}$ is the inverse of $a b$ modulo $m$, i.e., $(a b)^{-1} \equiv a^{-1} b^{-1}(\bmod m)$. In particular, for any positive integer $k,\left(a^{k}\right)^{-1} \equiv\left(a^{-1}\right)^{k}(\bmod m)$.