  We show that the differential complex $\Omega_{B}$ over the braided matrix
algebra $BM_{q}(N)$ represents a covariant comodule with respect to the
coaction of the Hopf algebra $\Omega_{A}$ which is a differential extension of
$GL_{q}(N)$. On the other hand, the algebra $\Omega_{A}$ is a covariant braided
comodule with respect to the coaction of the braided Hopf algebra $\Omega_{B}$.
Geometrical aspects of these results are discussed.
