Something that inhibits my understanding of a lot of the things beyond section 2.6: according to the article, equation 4b is supposed to also work for scalar ^

Something that inhibits my understanding of a lot of the things beyond section 2.6: according to the article, equation 4b is supposed to also work for scalar ^ vector and scalar ^ scalar, but both those cases seem to contradict defn 20. - according to 4b, scalar ^ scalar will always be 0 (a^b = (ab - ba)/2 = 0, since scalar multiplication commutes), same for scalar ^ vector (a^V = (aV - Va)/2 = 0, since scalar times vector also commutes). Definition 20 on the other hand makes sense (scalar ^ scalar is a regular multiplication, same for scalar ^ vector where it's just scaling). Am I missing something? Why does 4b try to generalize to grades <= 1 in a way that contradicts the other definition (and is counter-intuitive to me)? It all makes sense if 4b only applies to grades = 1.