This answer is not correct. You can always remember whether an element is oxidized or reduced by thinking of the saying; "LEO the lion goes GER". A Loss of Electrons is Oxidation and a Gain of Electrons is Reduction. The bromine atoms are gaining electrons to go to bromide ions...therefore they are reduced. The zinc loses electrons to go to the zinc cation...therefore it is oxidized.
The element or compound that is oxidized is not the "agent" that does the oxidizing. The oxidizing agent is the element or compound that is reduced.