  We construct a linear representation of the group IA(F_n) of IA-automorphisms
of a free group F_n, an extension of the Gassner representation of the pure
braid group P_n. Although the problem of faithfulness of the Gassner
representation is still open for n > 3, we prove that the restriction of our
representation to the group of basis conjugating automorphisms Cb_n contains a
non-trivial kernel even if n=2. We construct also an extensions of the Burau
representation to the group of conjugating automorphisms C_n. This
representation is not faithful for n > 1.
