  Linear arithmetics are extensions of Presburger arithmetic (Pr) by one or
more unary functions, each intended as multiplication by a fixed element
(scalar), and containing the full induction schemes for their respective
languages. In this paper we construct a model M of the 2-linear arithmetic LA_2
(linear arithmetic with two scalars) in which an infinitely long initial
segment of "Peano multiplication" on M is 0-definable. This shows, in
particular, that LA_2 is not model complete in contrast to theories LA_1 and
LA_0=Pr that are known to satisfy quantifier elimination up to disjunctions of
primitive positive formulas. As an application, we show that M, as a discretely
ordered module over the discretely ordered ring generated by the two scalars,
is not NIP, answering negatively a question of Chernikov and Hils.
