  I establish the relation of the non-commutative BV-formalism with
super-invariant matrix integration. In particular, the non-commutative
BV-equation, defining the quantum A-infinity-algebras, introduced in "Modular
operads and Batalin-Vilkovisky geometry" IMRN, Vol. 2007, doi:
10.1093/imrn/rnm075, is represented via de Rham differential acting on the
matrix spaces related with Bernstein-Leites simple associative algebras with
odd trace q(N), and with gl(N|N). I also show that the Lagrangians of the
matrix integrals from "Noncommmutative Batalin-Vilkovisky geometry and Matrix
integrals", Comptes Rendus Mathematique, vol 348 (2010), pp. 359-362,
arXiv:0912.5484, are equivariantly closed differential forms.
