Understanding of example of subspacee

Question

Let F be a field. Then, { (a,b) $\in$ F: $\alpha$a+$\beta$b=0} is a subspace of FxF for any $\alpha$, $\beta$ $\in$ F.

My question is that can be FxF is a subspace of f? If not, why?

Answer 1

First ask yourself is F×F a subset of F. And youll get the answer immediately