  In this paper we consider an electron moving on a two dimensional
noncommutative plane immersed in a constant magnetic field under the influence
of an anisotropic harmonic potential. We work out the gauge invariant energy
spectra of this system using a consistent gauge prescription proposed in
\cite{nctori,gauge-wigfunc}. We also show subsequently that straightforward
generalization of the Landau problem in the noncommutative setting using
minimal coupling prescription as is done naively on many occasions in the
literature violates gauge invariance of the energy spectra.
