# If * is a binary operation defined by a*b=$\frac{ab}{100}$ in $Q^+$ then the inverse element of 0.1 is:

$\begin{array}{1 1} 10^3 \\ 10^4 \\ 10^5 \\ 10^6 \end{array}$

Toolbox:
• If $e\in Q^+$ is the identity element , then $a*e=a \:\:\forall\:a\in\: Q^+$
• If $a*b=b*a=e$, where e is the identity element of * then b is inverse of a and viceversa.
Let e be the identity element then
$a*e=a\:\Rightarrow \large\frac{ae}{100}=a$
$\Rightarrow e=100$
Let $x$ be the inverse element of 0.1
Then $0.1*x=100$ $\Rightarrow\:\large\frac{0.1x}{100}=$$100$
$\Rightarrow\:x={10}^5$