Question

Identity of zero under multiplication is zero, because 0 ${}^{\ast }$ 0 = 0 = 0 ${}^{\ast }$ 0

• A. True
• B. False

Answer 1

The correct option is B

False

We know that if e is the identity of binary operation ${}^{\ast }$ , then a ${}^{\ast }$ e = a = e ${}^{\ast }$ a for all a. So for multiplication we get this as ae = a = ea. Even though when a = 0 and e = 0 satisfies this relation, that is 0.0 = 0 = 0.0. But e = 0 is not satisfied for other values of a, that is when a = 1, we get e =1. One important note is that identity is defined for a binary operation ${}^{\ast }$, not for each element of it. So, we can't have different identities for 0 and other elements(like 1 we saw). The value of e, which is true for all values of a is 1. That is a.1 = a = 1.a