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If $\left(G^{*}\right)$ is a group and the order of an element $a \in G$ is 10 , then the order of the inverse of $a$ * a is
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Verified Answer
The correct answer is:
10
We know that, let $(\mathrm{G}, 0)$ be a group \& e be the identity then
$\begin{aligned}
(\mathrm{a} * \mathrm{a})^{-1} &=\mathrm{a}^{-1} \mathrm{o} \mathrm{a}^{-1} \\
&=\left(\mathrm{a}^{-1}\right)^{-1}=\mathrm{a} .
\end{aligned}$
$\begin{aligned}
(\mathrm{a} * \mathrm{a})^{-1} &=\mathrm{a}^{-1} \mathrm{o} \mathrm{a}^{-1} \\
&=\left(\mathrm{a}^{-1}\right)^{-1}=\mathrm{a} .
\end{aligned}$
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