Question

Which of the following is the identity pair of addition and multiplication in order?

• A. (0,1)
• B. (1,1)
• C. (1,0)
• D. (0,0)

Answer 1

The correct option is A

(0,1)

1. If e is the identity of a binary operation, then a ${}^{\ast }$ e = a = e ${}^{\ast }$ a for all a from the set on which it is defined. Let e1 be the identity of multiplication, then a.e1 = a = e1.a From this relation we can find the value of e1, which is 1. So the identity of multiplication is 1. If e2 is the identity of addition, then a+e2 = a = e2+a. From this we get e2 = 0. So 0 is the identity of addition. So the identity pair of addition and multiplication is (0,1)