Previous year gate question [closed]

Question

For the set N of natural numbers and a binary operation f : N x N → N, an element z ∊ N is called an identity for f, if f (a, z) = a = f(z, a), for all a ∊ N. Which of the following binary operations have an identity?

1. f (x, y) = x + y - 3
2. f (x, y) = max(x, y)
3. f (x, y) = x^y

I have  query to option II f(2,7) here a=2 , z=7 so f(2,7)=max(2,7)=2 which is not right ......is my approach right ?

Comments

option 2) has an identity element as 1..

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Give clarification.