Vector space/One axiom missing/Identity/Example/Exercise

Give an example of a field ${}K$, a commutative group ${}(V,+,0)$, and a mapping

$K\times V\longrightarrow V,(s,v)\longmapsto sv,$

such that this structure fulfills all vector space axioms, with the exception of

$(5)\,\,\,1u=u.$

Create a solution