Question

Which of the following is the inverse pair of 1 under the operations multiplication and subtraction?

• A. 1,1
• B. 1,0
• C. 0,0
• D. None of these

Answer 1

The correct option is D

None of these

If we want to find the inverse of an element under the binary operation ${}^{\ast }$, then ${}^{\ast }$ should have an identity. This is clear from the definition of inverse for an element. If e is the identity of ${}^{\ast }$ and a ${}^{\ast }$ b = e = b ${}^{\ast }$ a, then b is called the inverse of a. But we saw that subtraction does not have an identity. So the inverse for any element under subtraction does not exist.

$\Rightarrow$ None of these