Noncommutative Geometry from 0-branes in a Background B-field

We study 0-branes in type IIA on $T^2$ with a background B-field turned on. This enables us to find the matrix model for M-theory on $T^2$ with a background 3-form potential along the torus and the lightlike circle. The theory is a non-local 2+1 dim SYM theory on a dual $T^2$ exactly as proposed by Connes,Douglas and Hull. We calculate the radii and the gauge coupling for the SYM on the dual $T^2$ for all choices of longitudinal momentum and membrane wrapping number on the $T^2$.