The product of the oxidation of I$^-$ with MnO$_4^-$ in alkaline medium is:
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In oxidation reactions with MnO$_4^-$, the halide is typically oxidized to a higher oxidation state, often leading to periodate (IO$_4^-$) in alkaline conditions.
In an alkaline medium, the oxidation of iodide ions (I$^-$) by permanganate ions (MnO$_4^-$) yields iodate (IO$_3^-$) and subsequently periodate (IO$_4^-$). This exemplifies the characteristic oxidation of halides by MnO$_4^-$ under basic conditions. Therefore, the resultant product is IO$_4^-$, corresponding to option (A).