Concept:
Hydrogen peroxide (H$_2$O$_2$) acts as both oxidizing and reducing agent depending on the medium and the species it reacts with. With strong oxidizing agents like periodate (IO$_4^{-}$), it acts as a reducing agent.
Step 1: Redox reaction
In alkaline medium:
\[
IO_4^{-} + H_2O_2 \rightarrow IO_3^{-} + H_2O + O_2
\]
Step 2: Oxidation states
• Iodine: +7 in IO$_4^{-}$ → +5 in IO$_3^{-}$ (reduction)
• Oxygen in H$_2$O$_2$: -1 → 0 in O$_2$ (oxidation)
Step 3: Final products
Potassium iodate (KIO$_3$), water, and oxygen gas.
Thus correct option is (A).