  Noncommutative torus compactification of Matrix model is shown to be a direct
consequence of quantization of the open strings attached to a D-membrane with a
non-vanishing background $B$ field. We calculate the BPS spectrum of such a
brane system using both string theory results and DBI action. The DBI action
leads to a new transformation property of the compactification radii under the
$SL(2,Z)_N$ transformations.
