  In this paper we show that when $\mathrm{G}$ is a classical semi-simple
algebraic group, $\mathrm{B}\subset\mathrm{G}$ a Borel subgroup, and
$\mathrm{X} = \mathrm{G}/\mathrm{B}$, then the structure coefficients of the
Belkale-Kumar product $\odot_{0}$ on $\mathrm{H}^{*}(\mathrm{X}, \mathbf{Z})$
are all either $0$ or $1$.
