An oxidising agent is one which oxidises(oxidation number increases) others and itself gets reduced. Whereas a reducing agent reduces (oxidation number decreases) others and itself gets oxidised.
The oxidising state of the oxygen atom on H2O2 is -1 which is an intermediate state. It means that it can either reduce itself to H2O where oxidation state of O is -2 or it can oxidise itself to O2, where the oxidation state of O is 0.
So, we can see that H2O2 acts as an oxidising agent in the first reaction as it increases the oxidation number of I- in HI from -1 to 0 in I2.
Similarly, H2O2 acts as a reducing agent in the second reaction as it decreases the oxidation number of Cl+ in HOCl from +1 to -1 in Cl-.
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