Let F be a field.
Consider. As is the multiplicative group of nonzero elements of F, this implies:
(By the definition of identity)
Consider . As , the multiplicative group of nonzero elements of F, acts on the set F by where and is usual product of two field elements, this implies:(By the associatively of multiplication in F)
By the definition of identity and the associativity of multiplication in F, left multiplication by nonzero element is in fact the group action.