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if $A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]$ then the matrix $A^{- 50}$ when $θ = \frac{π}{12}$ is equal to

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1232−3212

32−121232

3212−1232

12−323212

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detailed solution

Correct option is C

We haveA-1=cosθsinθ-sinθcosθ⇒A-1n=cosnθsinnθ-sinnθcosnθ⇒A-50=cos50θsin50θ-sin50θcosn50θ⇒A-50=cos25π6sin25π6-sin25π6cos25π6 at θ=π12 =3212-1232

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if A=cosθ−sinθsinθcosθ then the matrix A−50when θ=π12 is equal to

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if $A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]$ then the matrix $A^{- 50}$ when $θ = \frac{π}{12}$ is equal to