Hydrogen peroxide acts both as an oxidizing and as a reducing agent, depending upon the nature of the reacting species. In which of the following cases ${\mathrm{H}}^2{\mathrm{O}}^2$ acts as a reducing agent in the acid medium?

In  ${\mathrm{MnO}}_4^{-}$, Mn has an oxidation state of +7. Only Mn can be reduced by H₂O₂ because  ${\mathrm{MnO}}_4^{-}$ contains Mn in its most oxidized state.

Hence, for  ${\mathrm{MnO}}_4^{-},{\mathrm{H}}_2{\mathrm{O}}_2$ acts as a reducing agent in an acid medium.

Hence, option A is correct.