Let R^2 be a set containing all possible rows: (a b) when using the 8 axioms to prove whether (a,b) is indeed a vector space, i have to show that there is a zero element and a unit element. Is the zero element 0? or is it in matrix form such that W = (0 0) and W is contained in R^2? Is the unit element 1? or is it in matrix form such that F=(1 1) and F is contained in R^2? If I showed the 8 axioms are true, then does that show that R^2 is indeed a vector space?