  We study the variations of the worldvolume fields in the non-Abelian action
for multiple D-branes. Using T-duality we find that the embedding scalars
transform non-trivially under NS-NS gauge transformations as \delta X ~ [X, X]
and prove that the non-Abelian Chern-Simons action is invariant under these
transformations. Given that T-duality relates the (part of the) NS-NS
transformation with (part of the) general coordinate transformations, we can
get some insight in the structure of non-Abelian coordinate transformations.
