We present several non-trivial examples of the three-dimensional quantum Na
mbu bracket which involve square matrices or three-index objects. Our examp
les satisfy two fundamental properties of the classical Nambu bracket: they
are skew-symmetric and they obey the Fundamental Identity. We contrast our
approach to the existing literature on the quantum deformations of Nambu m
echanics. We also discuss possible applications of our results in M-theory.