  We compute the Witten index of the Berenstein-Maldacena-Nastase matrix
quantum mechanics, which counts the number of ground states as well as the
difference between the numbers of bosonic and fermionic BPS states with nonzero
spins. The Witten index sets a lower bound on the entropy, which exhibits an
$N^2$ growth that predicts the existence of BPS black holes in M-theory,
asymptotic to the plane wave geometry. We also discuss a relation between the
Witten index in the infinite $N$ limit and the superconformal index of the
Aharony-Bergman-Jafferis-Maldacena theory.
