Let $$P=3/21/2$$â$$1/23/2$$,$$A=1$$ââââ$$10$$ââââ$$1$$ and $$Q=PAP$$â² then Pâ²$$Q2015P$$ is

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Let $$P=3/21/2$$â$$1/23/2$$,$$A=1$$ââââ$$10$$ââââ$$1$$ and $$Q=PAP$$â² then Pâ²$$Q2015P$$ is

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$$P=$$$$cos$$â¡$$($$Ï$$/6)$$$$sin$$â¡$$($$Ï$$/6)$$â$$sin$$â¡$$($$Ï$$/6)$$$$cos$$â¡$$($$Ï$$/6)$$â Pâ²$$=$$$$cos$$â¡$$($$Ï$$/6)$$â$$sin$$â¡$$($$Ï$$/6)$$$$sin$$â¡$$($$Ï$$/6)$$$$cos$$â¡$$($$Ï$$/6)Since$$ PPâ²$$=1$$ââââ$$00$$ââââ$$1$$âPâ²$$=P$$â$$1We$$ have $$Q=PAP$$â²$$=PAP$$â$$1$$â $$Q2015=PAP$$â$$12015=PA2015P$$â$$1Thus$$, Pâ²$$Q2015P=P$$â$$1PA2015P$$â$$1P=P$$â$$1PA2015P$$â$$1PNow$$, $$A=I+B$$ where $$B=0$$ââââ$$10$$ââââ$$0Since$$, $$B2=O$$, we get $$Br=O$$ârâ¥$$2Thus$$,  $$A2015=I+2015B=1201501$$

Let $P = [\begin{array}{cc} \sqrt{3} / 2 & 1 / 2 \\ â 1 / 2 & \sqrt{3} / 2 \end{array}], A = [\begin{array}{ll} 1 ââââ 1 \\ 0 ââââ 1 \end{array}]$ and $Q = P A P^{â²}$ then $P^{â²} Q^{2015} P$ is

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Let P=3/21/2â1/23/2,A=1â â â â 10â â â â 1 and Q=PAPâ² then Pâ²Q2015P is

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Let $P = [\begin{array}{cc} \sqrt{3} / 2 & 1 / 2 \\ â 1 / 2 & \sqrt{3} / 2 \end{array}], A = [\begin{array}{ll} 1 ââââ 1 \\ 0 ââââ 1 \end{array}]$ and $Q = P A P^{â²}$ then $P^{â²} Q^{2015} P$ is