Prove that the given functionis operation preserving.

Homomorphisms G is the group of 53rd roots of unity under complex multiplication. Z53 is the group of integers mod 53 under modular addition. 2nix Let elements in G be represented using exponential notation as e 53 , where x is an integer ranging from 0 to 52. 2nix Consider the function defined by fe 53 = [x]53 from G - Z53 A. Prove that the given function is operation preserving