How to find if neutral/idnty element exists for 16 different binary operations of *?

Suppose I'm given an operation on a set such that the operation between two elements of set is also an element of set

Now there are possible binary operations of on set .

If I'm asked to find if there exists a neutral/identity element of a certain table where

are defined, how do I figure that out?

What I mean is suppose 1 of 16 table of operations looks like this:

How do I figure out if an identity element exist for this table? Also is it possible to find the identity/neutral element from this table?

Re: How to find if neutral/idnty element exists for 16 different binary operations of

That binary operation does not have an identity. The definition of identity is "e is an identity for operation "*" if and only if e*x= x*e= x for every x in in the set". Here, a*b= b but so a is NOT an identity. Similarly, b*a= a but so b is not an identity.

Re: How to find if neutral/idnty element exists for 16 different binary operations of