is two dimensional since , which means that is a vector space with two entries.
It's clear that
Now using the definition of subspace:
Since
and is closed under addition and scalar multiplication is a two dimensional subspace of
Your question is imprecise. First, if is the field , then it is unclear over what field you are considering to be a vector space. For instance it's a 6-dimensional vector space over , but a 3-dimensional one over . You always need to specify the underlying field. Haven, above, assumed that the vector space is over . Check your question!
Noting Bruno's comment on fields. If we assume is an vector space, then my above answer is correct. However if we view as a vector space. Then an example of a two-dimensional vector space would be
I assume based on the vagueness of the question that you are in a Linear Algebra class and you have little or no understanding of what a field is (in the context of the class). So the interpretation of as an vector space, is probably the desired one.