  In this paper we consider IIA and IIB matrix string theories which are
defined by two-dimensional and three-dimensional super Yang-Mills theory with
the maximal supersymmetry, respectively. We exactly compute the partition
function of both of the theories by mapping to a cohomological field theory.
Our result for the IIA matrix string theory coincides with the result obtained
in the infra-red limit by Kostov and Vanhove, and thus gives a proof of the
exact quasi classics conjectured by them. Further, our result for the IIB
matrix string theory coincides with the exact result of IKKT model by Moore,
Nekrasov and Shatashvili. It may be an evidence of the equivalence between the
two distinct IIB matrix models arising from different roots.
