  As an extension to our earlier work \cite{Mirza2}, we employ the Nambu
brackets to prove that the divergences of heat capacities correspond to their
counterparts in thermodynamic geometry. We also obtain a simple representation
for the conformal transformations that connect different thermodynamics metrics
to each other. Using our bracket approach, we obtain interesting exact
relations between the Hessian matrix with any number of parameters and specific
heat capacities. Finally, we employ this approach to investigate some
thermodynamic properties of the Meyers-Perry black holes with three spins.
