Question

Let $*$ be a binary operation on the set $Q$ of rational numbers defined by $a*b$ = $\frac{ab}{4}$ . The identity with respect to this operation is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Given that,
${* }$ be a binary operation on the set of rational numbers
and $a^{*}b=\frac{ab}{4}$
By inspection, we get ?4? is the identity elements with respect to $?*?$ operation
Let $a^{*}e=a=e^{*}a$,
where $e$ is identity element
$\therefore$ $a^{*}e=\frac{ae}{4}=a$
$\Rightarrow a^{*}e=\frac{ae}{4}=a$
$\Rightarrow ae-4a=0$
$\Rightarrow a(e-4)=0$
$\Rightarrow e=4 \ne 0$
$0\notin Q$
Hence, identity element $(e) = 4$