[en] The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R cap (p), where p stands for a set of mutually commuting variables. A family of SL (n)-type solutions of this equation provides a new realization of the Hecke algebra. We define quantum antisymmetrizers, introduce the notion of quantum determinant and compute the inverse quantum matrix for matrix algebras of the type R cap (p) a₁a₂ = a₁a₂R cap. It is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the WZNW model