Question

An identity element of a group has ______ element.

(a) associative

(b) commutative

(c) inverse

(d) homomorphic

The question was posed to me during an online interview.

The doubt is from Groups in section Groups of Discrete Mathematics

Answer 1

Right choice is (c) inverse

To elaborate: By the definition of all elements of a group have an inverse. For an element, a in a group G, an inverse of a is an element b such that ab=e, where e is the identity in the group. The inverse of an element is unique and usually denoted as -a.