Show that in a field K {\displaystyle {}K} , the following properties hold.
(1) For every a ∈ K {\displaystyle {}a\in K} , the mapping
is bijective.
(2) For every b ∈ K {\displaystyle {}b\in K} , b ≠ 0 {\displaystyle {}b\neq 0} , the mapping