  A key step towards dissipationless transport devices is the quantum anomalous
Hall effect, which is characterized by an integer quantized Hall conductance in
a ferromagnetic insulator with strong spin-orbit coupling. In this work, the
anomalous Hall effect due to the impurity scattering, namely the extrinsic
anomalous Hall effect, is studied when the Fermi energy crosses with the
topologically nontrivial conduction band of a quantum anomalous Hall system.
Two major extrinsic contributions, the side-jump and skew-scattering Hall
conductivities, are calculated using the diagrammatic techniques in which both
nonmagnetic and magnetic scattering are taken into account simultaneously. The
side-jump Hall conductivity changes its sign at a critical sheet carrier
density for the nontrivial phase, while it remains sign unchanged for the
trivial phase. The critical sheet carrier densities estimated with realistic
parameters lie in an experimentally accessible range. The results imply that a
quantum anomalous Hall system could be identified in the good-metal regime.
