Singularities of determinantal pure pairs

Let X be a generic determinantal affine variety over a perfect field of characteristic p >= 0 and P subset of X be a standard prime divisor generator of Cl X congruent to 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 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 Q-divisor Delta with coefficients in [0, 1) such that ( X, P + Delta) is PLT.