Hydrogen peroxide in its reaction with $KI{O}_4$ and $N{H}_{2}OH$ respectively, is acting as:

The correct option is A

A reducing agent, an oxidizing agent

Let us look at the reactions one at a time:

$N{H}_{2}OH+H_2{O}_2⟶N_2{O}_3+H_{2}O$

In this reaction, nitrogen is oxidized from (-1) to (+3).
Hence, $H_2{O}_2$ is an oxidizing agent.

In the other case, it reduces iodine from (+7) to (+5):

$KI{O}_4+H_2{O}_2⟶KI{O}_3+H_{2}O+O_2$