  Using two approaches to strongly correlated systems, the extremely correlated
Fermi liquid theory and the dynamical mean field theory, we compute the
transverse transport coefficients, namely the Hall constants $R_H$ and Hall
angles $\theta_H$, and also the longitudinal and transverse optical response of
the $U=\infty$ Hubbard model in the limit of infinite dimensions. We focus on
two successive low-temperature regimes, the Gutzwiller correlated Fermi liquid
(GCFL) and the Gutzwiller correlated strange metal (GCSM). We find that the
Hall angles $\cot \theta_H \propto T^2$ in the GCFL regime, on warming into the
strange metal regime, it passes through a downward bend and continues as $T^2$.
Equivalently, $R_H$ is weakly temperature dependent in the GCFL regime, and
becomes strongly $T$-dependent in the GCSM regime. Drude peaks are found for
both the longitudinal optical conductivity $\sigma_{xx}(\omega)$ and the
optical Hall angles $\tan \theta_H(\omega)$ below certain characteristic energy
scales. By comparing the relaxation rates extracted from fitting to the Drude
formula, we find that in the GCFL regime there is a single relaxation rate
controlling both longitudinal and transverse transport, while in the GCSM
regime two independent relaxation rates emerge. We trace the origin of this
behavior to the dynamical particle-hole asymmetry of the Dyson self-energy,
arguably a generic feature of doped Mott insulators.
