Noncommutative geometry from strings and branes

Noncommutative torus compactification of Matrix model is shown to be a dire ct 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 DB I action leads to a new transformation property of the compactification rad ii under the SL(2, Z)(N) transformations.