  The Magnus representation of the Torelli subgroup of the mapping class group
of a surface is a homomorphism r: I_{g,1} -> GL_{2g}(Z[H]). Here H is the first
homology group of the surface. This representation is not faithful; in
particular, Suzuki previously described precisely when the commutator of two
Dehn twists about separating curves is in the kernel of r. Using the trace of
the Magnus representation, we apply a new method of showing that two
endomorphisms generate a free group to prove that the images of two positive
separating multitwists under the Magnus representation either commute or
generate a free group, and we characterize when each case occurs.
