The product of oxidation of ${\mathrm{I}}^{-}$with ${\mathrm{MnO}}_4^{-}$ in alkaline medium is :

${\mathrm{I}}^{-}$ oxidation with ${\mathrm{MnO}}_4^{-}$ is caused by,

Reaction : 

 $\begin{array}{r}\underset{+5}{{\mathrm{MnO}}_4^{-}}+{\mathrm{I}}^{-}\to {\mathrm{IO}}_3^{-}+{\mathrm{Mn}}^{+2}\\ \end{array}$

The product is in ${\mathrm{IO}}_3^{-}$ form.

Hence, the correct option is A.