Step 1: Understand disproportionation reaction.
A disproportionation reaction is a type of redox reaction in which the same substance undergoes both oxidation and reduction simultaneously.
Step 2: Analyze option (A).
In \( H_2O_2 \), oxygen has oxidation state \( -1 \).
After reaction:
In \( H_2O \), oxygen is \( -2 \) (reduction)
In \( O_2 \), oxygen is \( 0 \) (oxidation)
Thus, the same element oxygen is both oxidized and reduced.
Step 3: Check other options.
(B) \( KMnO_4 \) decomposes but manganese does not undergo both oxidation and reduction in the same way.
(C) This is a redox reaction between two different species, not disproportionation.
(D) This is a displacement reaction, not disproportionation.
Step 4: Conclusion.
Only option (A) shows the same substance undergoing both oxidation and reduction.
Therefore:
\[
\boxed{2H_2O_2 \rightarrow 2H_2O + O_2}
\]