Past exam of the model theory course of the University of Oxford / 2011 / 1 / b / i / γ / Solution

No. Definability of a function means definability of its graph. The same additive structure automorphism $s(x)=-x$ would have to preserve the graph of multiplication. It sends the graph point $(1,1,1)$ to $(-1,-1,-1)$, which is not a multiplication-graph point because $(-1)(-1)=1\ne -1$. This contradicts automorphism invariance of parameter-free definability.