If $a * b=10$ ab on $Q^{+}$ then find the inverse of 0.01
If $a * b=10$ ab on $Q^{+}$ then find the inverse of 0.01
Let $e$ be the identity element for $*$.
$\therefore a * e=a=e * a$
$\therefore a e=a \Rightarrow e=\frac{1}{10}$
Let $a^{\prime}$ be the inverse of $0.01 .$
$\therefore 0.01 * a^{\prime}=e$
$\therefore 10 \times \frac{1}{100} \times a^{\prime}=\frac{1}{10}$
$\Rightarrow a^{\prime}=1$
$\therefore$ Inverse of 0.01 is $1 .$
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