Question

an element b is said to be inverse of a if​

Answer 1

Answer:

An inverse of an element is another element in the set that, when combined on the right or the left through the operation, always gives the identity element as the result. ... For any element x of the set, there is another element y of the set so that x#y = e and y#x = e

Answer 2

Answer:

• An inverse element for a is an element which gives the identity when composed with a.

Explanation:

let $ be a set, # is a binary operation on $ and a∈$. Suppose that there is an identity element e for the operation. Then

• an element b is a left inverse for a if b#a = e;

• an element b is a right inverse for a if a#b=e;

Hence, an element b is an inverse (or two-sided inverse) for a if it is both a left and right inverse for a.

We can say, If e is the identity of # and a #  b = e = b # a , then b is called the inverse of a.