Can I state that every linearly independent set of vectors that is independent in V and of length equal to dimension of V span the whole V?

Question

I know that

(A) if a set of vectors is linearly independent in vector space V and span the whole V, then this set forms a basis for V.

But I'm curious... (B) For a set to be basis, isn't it enough for this set to be independent and have length equal to dimension of V?