Question

The inverse of the number 5 with respect to the binary operation * defined by $a\ast b=4ab$ is .

• A. $\frac{1}{80}$
• B. $\frac{1}{5}$
• C. $\frac{1}{20}$

Answer 1

The correct option is A $\frac{1}{80}$

Let e be the identity
Then, $a\ast e.=a$
$\Rightarrow 4ae=a$
$\Rightarrow e=\frac{1}{4}$

Now, if x is the inverse of 5, then
$5\ast x=e$
$\Rightarrow 4\times 5\times x=\frac{1}{4}$
$\Rightarrow x=\frac{1}{4\times 4\times 5}$
$\Rightarrow x=\frac{1}{80}$