I derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to finite energies and gives the first non-trivial bound on 〈TrX2〉. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. The best lower bounds are already a factor of ~ 0.7 from the large N extrapolation of Monte Carlo predictions.