  The notion of a quasideterminant and a quasiminor of a matrix A=(a_{ij}) with
not necessarily commuting entries was introduced recently by I.Gelfand and the
second author. The ordinary determinant of a matrix with commuting entries can
be written (in many ways) as a product of quasiminors. Furthermore, it was
noticed by a number of authors that such well-known noncommutative determinants
as the Berezinian, the Capelli determinant, the quantum determinant of the
generating matrix of the quantum group U_h(gl_n) and the Yangian Y(gl_n) can be
expressed as products of commuting quasiminors.
  The aim of this paper is to extend these results to a rather general class of
Hopf algebras given by the Faddeev-Reshetikhin-Takhtajan type relations -- the
twisted quantum groups. Such quantum groups arise when Belavin-Drinfeld
classical r-matrices are quantized. Our main result is that the quantum
determinant of the generating matrix of a twisted quantum group equals the
product of commuting quasiminors of this matrix.
