${\mathrm{KMnO}}_4$  acts as an oxidising agent in

The compound  which act as oxidising agent that will oxidise other and reduce itself. Since potassium permanganate( ${\mathrm{KMnO}}_4$)may change its oxidation state from +7 to +6,+4,+2, it can operate as an oxidant in all media. 

$$\begin{gathered} \mathrm{Acidic} \mathrm{medium}: {\mathrm{MnO}}_4^{-}+5{\mathrm{e}}^{-}+8{\mathrm{H}}^{+}\to {\mathrm{Mn}}^{+2}+4{\mathrm{H}}_2\mathrm{O} \\ \mathrm{Basic} \mathrm{medium}: {\mathrm{MnO}}_4^{-}+{\mathrm{e}}^{-}\to {\mathrm{MnO}}_4^{2-} \\ \mathrm{Neutral} \mathrm{medium}: {\mathrm{MnO}}_4^{-}+4{\mathrm{H}}^{+}+3{\mathrm{e}}^{-}\to {\mathrm{MnO}}_2+{\mathrm{H}}_2\mathrm{O} \end{gathered}$$