  We generalize Dykhne's calculation of the effective resistance of a 2D
two-component medium to the case of frictional drag between the two parallel
two-component layers. The resulting exact expression for the effective
transresistance, $\rho^D_{eff}$, is analyzed in the limits when the resistances
and transresistances of the constituting components are strongly different -
situation generic for the vicinity of the {\em classical} (percolative)
metal-insulator transition (MIT). On the basis of this analysis we conclude
that the evolution of $\rho^D_{eff}$ across the MIT is determined by the type
of correlation between the components, constituting the 2D layers. Depending on
this correlation, in the case of two electron layers, $\rho^D_{eff}$ changes
either monotonically or exhibits a sharp maximum. For electron-hole layers
$\rho^D_{eff}$ is negative and $|\rho^D_{eff}|$ exhibits a sharp minimum at the
MIT.
