Signum Function of Reciprocal

Theorem
Let $x \in \R$ such that $x \ne 0$.

Then:
 * $\operatorname{sgn} \left({x}\right) = \operatorname{sgn} \left({\dfrac 1 x}\right)$

where $\operatorname{sgn} \left({x}\right)$ denotes the signum of $x$.