Apologies in advance for this spectacularly uninteresting question, but it has just come up in my work. (Okay, not in a truly important way, but I am trying to gauge the scope of a certain construction.)

Let $K$ be a field and $A$ be a division Albert algebra over $K$, i.e., a certain kind of $27$-dimensional commutative Jordan algebra over $K$.

Is it true that for all nonzero elements $x,y \in A$, one has $(xy) y^{-1} = x$?

Note that this is true in any finite-dimensional division algebra in which each subalgebra generated by two elements is associative, in particular in any composition algebra. But so far as I know (and by the way I know nothing about Albert algebras!), this "2-associativity" property does not hold here.