Mark the correct alternative in each of the following:
For the binary operation * on Z defined by a * b = a + b + 1 the identity element is
For Identity element a * e = a = e * a , with ‘e’ being the identity element.
Given a * b = a + b + 1
⇒ a * e = a + e + 1 = a ….(1)
⇒ e * a = e + a + 1 = a …. (2)
⇒ e = -1 is the required identity element.