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

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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 $S$:

\(\ds \paren {-1}^{-1}\) \(=\) \(\ds -1\)
\(\ds 2^{-1}\) \(=\) \(\ds \dfrac 1 2\)

$\blacksquare$


Sources