# Prove that the field F is a vector space over itself.

How can I prove that a field F is a vector space over itself?
Intuitively, it seems obvious because the definition of a field is
nearly the same as that of a vector space, just with scalers instead
of vectors.

Here’s what I’m thinking:
Let V={(a)|a in F} describe the vector space for F. Then I just show
that vector addition is commutative, associative, has an identity and
an inverse, and that scalar multiplication is distributaries,
associative, and has an identity.

x,y in V
(x)+(y)=(y)+(x)
(X+y)=(x+y) associative property

x,y,0 in V
(x)+(y)=(0)