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Question Number 12291 by 1kanika# last updated on 18/Apr/17

Answered by 433 last updated on 07/May/17

$$\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\times \left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]=A$$$$\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\times \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]=-A$$$$\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\times \left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]=-I_2$$$${\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]}^2=I_2$$$$A^2=I_2$$$$G=\{\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],A,-A,I,-I\}$$$$ord\left(G\right)=6$$

Commented by 1kanika# last updated on 02/Jun/17

$$\mathrm{sir}\mathrm{it}\mathrm{can}\mathrm{also}\mathrm{solve}\mathrm{by}\mathrm{taken}\mathrm{LCM}\mathrm{of}$$$$\mathrm{order}\mathrm{of}\mathrm{generated}\mathrm{matrices}.$$

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