$\displaystyle A= \left( \begin{matrix} i & 0 \\ 0 & -i \end{matrix} \right) $

, $\displaystyle B= \left( \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right) $

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Show that $\displaystyle \langle A, B \rangle$ is subgroup of $\displaystyle GL_2(\mathbb{C})$. And Show that $\displaystyle \langle A, B \rangle$ generated by $\displaystyle A$ and $\displaystyle B$, and order of $\displaystyle \langle A, B \rangle$ is 8 ?