Question

Verify that ${\mathit{A}}_{\mathbf{2}}\mathbf{=}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$.

Short answer

It is proved that,$A_2=\left\{\left(1\right)\right\}$.

Step-by-step solution

Determine that A2=(1)

Consider that $A_2\left(1\right)$.

The order of$A_n$ is $\frac{n!}{2}$.

Applying formula

Now, applying this to the order of$A_2$ as:

$\begin{array}{c}\frac{2!}{2}=\frac{2}{2}\\ =1\end{array}$

Thus, $A_2=\left\{\left(1\right)\right\}$.