Question

In a group (G, *), for some element 'a' of G, if $a^2=e$, where e is the identity element, then

• A. $a=a^{-1}$
• B. $a=\sqrt{e}$
• C. $a=\frac{1}{a^2}$
• D. $a=e$

Answer 1

The correct option is A $a=a^{-1}$

Let the element be $a$ from the group $G$

Given $a^2=e$

Now $a^{\ast }a=a^{\ast }{a}^{-1}$ [By definition]

$\Rightarrow a=a^{-1}$ [Cancelling $a$ from each side]