If A = beginbmatrix cosθ & -sinθ \ sinθ & cosθ endbmatrix, then the matrix A^-50 when θ = (π)/12, is equal to

beginbmatrix dfrac√(3)2 & 1/2 \ -1/2 & dfrac√(3)2 endbmatrix

beginbmatrix 1/2 & dfrac√(3)2 \ -dfrac√(3)2 & 1/2 endbmatrix

beginbmatrix dfrac√(3)2 & -1/2 \ 1/2 & dfrac√(3)2 endbmatrix

beginbmatrix 1/2 & -dfrac√(3)2 \ dfrac√(3)2 & 1/2 endbmatrix

If A = beginbmatrix cosθ & -sinθ \ sinθ & cosθ endbmatrix,… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 9 Jan · Shift I

A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}

, then the matrix

A^{-50}

when

\theta = \dfrac{\pi}{12}

, is equal to

A.
$\begin{bmatrix} \dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \\ -\dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \end{bmatrix}$
B.
$\begin{bmatrix} \dfrac{\sqrt{3}}{2} & -\dfrac{1}{2} \\ \dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$
C.
$\begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \\ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$
D.
$\begin{bmatrix} \dfrac{1}{2} & -\dfrac{\sqrt{3}}{2} \\ \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \end{bmatrix}$

Show answer

Correct option: C

[JEE Main 2019 · 9 Jan · Shift I]

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