Duality and Serre functor in homotopy categories

For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories ${$\mathbb{K}$}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm op}})$and${$\mathbb{K}$}^{{\rm{b}}}({\rm mod}{\mbox{-}}A)$\mathrm{.}If$A=\Lambda$ is an artin algebra of finite global dimension, this duality restricts to a duality between their subcategories of acyclic complexes, ${\mathbb{K}}_{\mathrm{a}\mathrm{c}}^{\mathrm{b}}(\mathrm{m}\mathrm{o}\mathrm{d}-{\mathrm{\Lambda }}^{\mathrm{o}\mathrm{p}})$ and ${\mathbb{K}}_{\mathrm{a}\mathrm{c}}^{\mathrm{b}}(\mathrm{m}\mathrm{o}\mathrm{d}-\mathrm{\Lambda })\mathrm{.}$ As a result, it will be shown that, in this case, ${$\mathbb{K}$}_{\rm ac}^{{\rm{b}}}({\rm mod}{\mbox{-}}\Lambda)$ admits a Serre functor and hence has Auslander-Reiten triangles.