  Let $X$ be a generic determinantal affine variety over a perfect field of
characteristic $p \geq 0$ and $P \subset X$ be a standard prime divisor
generator of $\mathrm{Cl}(X) \cong \mathbb{Z}$. We prove that the pair $(X,P)$
is purely $F$-regular if $p>0$ and so that $(X,P)$ is purely log terminal (PLT)
if $p=0$ and $(X,P)$ is log $\mathbb{Q}$-Gorenstein. In general, using recent
results of Z. Zhuang and S. Lyu, we show that $(X,P)$ is of PLT-type, i.e.
there is a $\mathbb{Q}$-divisor $\Delta$ with coefficients in $[0,1)$ such that
$(X,P+\Delta)$ is PLT.
