If A = begin{bmatrix} cos theta & sin theta | vedclass

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(D) Given $A = \begin{bmatrix} \cos 	heta & \sin 	heta \ -\sin 	heta & \cos 	heta \end{bmatrix}$.We know that for a rotation matrix $R(	heta) =

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$\sin 3 	heta, -\sin 3 	heta$

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(D) Given $A = \begin{bmatrix} \cos 	heta & \sin 	heta \ -\sin 	heta & \cos 	heta \end{bmatrix}$.We know that for a rotation matrix $R(	heta) = \begin{bmatrix} \cos 	heta & \sin 	heta \ -\sin 	heta & \cos 	heta \end{bmatrix}$,the property $R(	heta)^n = R(n	heta)$ holds.Thus,$A^3 = \begin{bmatrix} \cos 3 	heta & \sin 3 	heta \ -\sin 3 	heta & \cos 3 	heta \end{bmatrix}$.Comparing this with the given matrix $A^3 = \begin{bmatrix} \cos 3 	heta & m \ n & \cos 3 	heta \end{bmatrix}$,we get $m = \sin 3 	heta$ and $n = -\sin 3 	heta$.Therefore,the correct option is $D$.

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$ and $A^3 = \begin{bmatrix} \cos 3 \theta & m \\ n & \cos 3 \theta \end{bmatrix}$,the values of $m$ and $n$ respectively are

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