Field/Bijectivity of one-sided operations/Exercise

Show that in a field ${}K$, the following properties hold.

(1) For every ${}a\in K$, the mapping

$\alpha _{a}\colon K\longrightarrow K,x\longmapsto x+a,$

is bijective.

(2) For every ${}b\in K$, ${}b\neq 0$, the mapping

$\mu _{b}\colon K\longrightarrow K,x\longmapsto bx,$

is bijective.

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