For the so-called source-probe configuration in Matrix theory, we prove the
following theorem concerning the power of supersymmetry (SUSY): let delta
be a quantum-corrected effective SUSY transformation operator expandable in
powers of the coupling constant g as delta = Sigma (n greater than or equa
l to0)g(2n delta (n)), where delta ((0)) is of the tree-level form. Then, a
part from an overall constant, the SUSY Ward identity delta Gamma = 0 deter
mines the off-shell effective action Gamma uniquely to arbitrary order of p
erturbation theory, provided that the SO(9) symmetry is preserved. Our proo
f depends only on the properties of the tree-level SUSY transformation laws
and does not require the detailed knowledge of quantum corrections. (C) 20
01 Elsevier Science B.V. All rights reserved.