  By turning on antisymmetric background fluxes, we study how multiple
M2-branes are coupled to them. Our investigation concentrates on the gauge
invariance conditions for the Myers-Chern-Simons action. Furthermore, the
dimensional reduction of M2-branes to D2-branes introduces more constraints on
the newly introduced tensors. Particularly, for the theory based on A_4
algebra, we are able to fix all components of them up to an overall
normalization constant. These results can not be simply obtained from the
previously proposed cubic matrix representation for this algebra. We also
comment on cubic matrices as the representations of 3-algebras.
