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Question Number 58480 by rahul 19 last updated on 23/Apr/19

Commented by kaivan.ahmadi last updated on 23/Apr/19

$$LetP=\left[\begin{array}{c}ab\\ cd\end{array}\right]$$$$\left[10\right]\left[\begin{array}{c}ab\\ cd\end{array}\right]=\left[ab\right]\Rightarrow a=b=\frac{-1}{\sqrt{2}}$$$$and$$$$\left[01\right]\left[\begin{array}{c}ab\\ cd\end{array}\right]=\left[cd\right]\Rightarrow c=\frac{-1}{\sqrt{2}},d=\frac{1}{\sqrt{2}}$$$$\Rightarrow P=\frac{-1}{\sqrt{2}}\left[\begin{array}{c}11\\ 1-1\end{array}\right]$$$$P^2=\frac{1}{2}\left[\begin{array}{c}11\\ 1-1\end{array}\right]\left[\begin{array}{c}11\\ 1-1\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}20\\ 02\end{array}\right]=I$$$$\Rightarrow P^4=P^6=P^8=I$$$$so\left(C\right)istrue,since$$$$P^8+P^6+P^4-P^2=I+I+I-I=2I$$$$$$

Commented by rahul 19 last updated on 24/Apr/19

$$thankusir.$$

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