Affine-linear mapping/Functorial properties/Fact

Let ${}K$ be a field, and let ${}E,F$ and ${}G$ denote affine spaces over the vector spaces ${}U,V$ and ${}W$ . Then the following statements hold.

The identity
$\operatorname {Id} _{E}\colon E\longrightarrow E$

is affine-linear.
The composition of affine-linear mappings
$E\longrightarrow F$

and

$F\longrightarrow G$

is again affine-linear.
For a bijective affine-linear mapping
$\psi \colon E\longrightarrow F,$

also the inverse mapping is affine-linear.
For ${}v\in V$ , the translation
$E\longrightarrow E,P\longmapsto P+v,$

is affine-linear.
A linear mapping is affine-linear.