We investigate in the Matrix theory framework, the subgroup of dualities of
the DLCQ of M-theory compactified on three-tori, which corresponds to T-du
ality in the auxiliary Type II string theory. We show how these dualities a
re realized in the supersymmetric Yang-Mills gauge theories on dual non-com
mutative three-tori. (C) 1999 Elsevier Science B.V.