Question

A binary operation can have inverse without identity

• A. True
• B. False

Answer 1

The correct option is B

False

In the definition of inverse we assume the existence of identity. So, we can't have inverse without identity. That is inverse is defined for only those binary operations which has an identity. Definition of inverse : If e is the identity of ${}^{\ast }$ and a ${}^{\ast }$ b = e = b ${}^{\ast }$a, then b is called the inverse of a