Prove that the inverse of the function $\displaystyle f : \mathbb{R} - \left\{-\frac{d}{c}\right\} \rightarrow \mathbb{R} - \left\{\frac{a}{c}\right\}$, $\displaystyle f(x) = \frac{ax + b}{cx + d}, ad - bc\neq 0$ is also a linear fractional function. Under what condition $\displaystyle f(x)$ coincides with its inverse.