In my Finite Math class we are studying clock addition. We are given

The following table represents the operation # on the set G = {a, b, c, d}

Given:

The following table represents the operation # on the set G = {a, b, c, d}

#a b c d

a a b c d

b b c d a

c c d a b

d d a b c

In my Finite Math course, I am asked to EXPLAIN why the element a in that the table above is the identify element. I have already shared that when the element a is hash-tagged or paired with other elements, the result is the other element. However, I am asked to EXPLAIN my results. My instructor is not interested in computation just the explanation. Please help me explain.