R to R/Linear/Mapping/Example

Let ${}a\in \mathbb {R}$ be fixed. This real number defines a mapping

$\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto ax.$

For ${}a=0$, this is the constant zero mapping. For ${}a\neq 0$, we have a bijective mapping; the inverse mapping is

$y\longrightarrow {\frac {1}{a}}y.$

Here, the inverse mapping has a similar form as the mapping itself.