  Building on previous work, we calculate the temperature- and
frequency-dependent {\it anomalous} Hall conductivity for the putative
multiband chiral superconductor $\Sr$ using a simple microscopic two-orbital
model without impurities. A Hall effect arises in this system without the
application of an external magnetic field due to the time-reversal-symmetry
breaking chiral superconducting state. The anomalous Hall conductivity is
nonzero only when there is more than one superconducting order parameter,
involving inter- as well as intra-band Cooper pairing. We find that such a
multiband superconducting state gives rise to a distinctive resonance in the
frequency-dependence of the Hall conductivity at a frequency close to the
inter-orbital hopping energy scale that describes hopping between Ru $d_{xz}$
and $d_{yz}$ orbitals. The detection of this feature, robust to temperature and
impurity effects in the superconducting phase, would thus constitute compelling
evidence in favour of a multiband origin of superconductivity in $\Sr$, with
strong superconductivity on the $\alpha$ and $\beta$ bands. The temperature
dependence of the Hall conductivity and Kerr rotation angle are studied within
this model at the one-loop approximation.
