  We present an elegant method to prove the invariance of the Chern-Simons part
of the non-Abelian action for N coinciding D-branes under the R-R and NS-NS
gauge transformations, by carefully defining what is meant by a background
gauge transformation in the non-Abelian world volume action. We study as well
the invariance under massive gauge transformations of the massive Type IIA
supergravity and show that no massive dielectric couplings are necessary to
achieve this invariance. We show that this result is consistent with (massive)
T-duality from the non-Abelian action for N D9-branes.
