  From the bicovariant first order differential calculus on inhomogeneous Hopf
algebra ${\cal B}$ we construct the set of right-invariant Maurer-Cartan
one-forms considered as a right-invariant basis of a bicovariant ${\cal
B}$-bimodule over which we develop the Woronowicz's general theory of
differential calculus on quantum groups. In this formalism, we introduce
suitable functionals on ${\cal B}$ which control the inhomogeneous commutation
rules. In particular we find that the homogeneous part of commutation rules
between the translations and those between the generators of the homogeneous
part of ${\cal B}$ and translations are controled by different R-matrices
satisfying nontrivial characteristic equations.
