Inverse of Subset/Group/Examples/Subset of Reals under Multiplication

Example of Inverse of Subset of Group
Let $\struct {\R, \times}$ be the multiplicative group of (non-zero) real numbers.

Let $S = \set {-1, 2}$.

Then the inverse $S^{-1}$ of $S$ is:
 * $S^{-1} = \set {-1, \dfrac 1 2}$

Proof
Taking each element of $S$: