I would like to show that given a field $F$ and a vector space $V=F$ (so we are viewing this field as a vector space), then $V$ has only two subspaces. I know that these two subspaces are $\{0\}$ and $V$ and I know how to show that each one of them is a subspace. However, my issue is to show that these two are the only subspaces. I have tried to assume that there is a third subspace other than these two and somehow arrive at a contradiction, but so far no luck. Would someone please be able to help?