Question

Find the identity of the operation a ${}^{\ast }$ b = $\frac{ab}{4}$

• A. 1
• B. 0
• C. 2
• D. 4

Answer 1

The correct option is D

4

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 e be the identity of ${}^{\ast }$, then a ${}^{\ast }$ e = a = e ${}^{\ast }$ a. We are given a ${}^{\ast }$ $b=\frac{ab}{4}$.

$\Rightarrow$ a ${}^{\ast }$ $e=\frac{ae}{4}$ . This is equal to a

$\Rightarrow \frac{ae}{4}=a$

$\Rightarrow$ e = 4

So 4 is the identity of the binary operation given