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

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(C) Given $A = \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix}$.To find $A^2$,we calculate $A 	imes A$:$A^2 = \

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$\begin{bmatrix} \cos 2\alpha & \sin 2\alpha \ -\sin 2\alpha & \cos 2\alpha \end{bmatrix}$

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(C) Given $A = \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix}$.To find $A^2$,we calculate $A 	imes A$:$A^2 = \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix} \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix}$Performing matrix multiplication:$A^2 = \begin{bmatrix} (\cos \alpha)(\cos \alpha) + (\sin \alpha)(-\sin \alpha) & (\cos \alpha)(\sin \alpha) + (\sin \alpha)(\cos \alpha) \ (-\sin \alpha)(\cos \alpha) + (\cos \alpha)(-\sin \alpha) & (-\sin \alpha)(\sin \alpha) + (\cos \alpha)(\cos \alpha) \end{bmatrix}$$A^2 = \begin{bmatrix} \cos^2 \alpha - \sin^2 \alpha & 2\sin \alpha \cos \alpha \ -2\sin \alpha \cos \alpha & \cos^2 \alpha - \sin^2 \alpha \end{bmatrix}$Using trigonometric identities $\cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha$ and $\sin 2\alpha = 2\sin \alpha \cos \alpha$:$A^2 = \begin{bmatrix} \cos 2\alpha & \sin 2\alpha \ -\sin 2\alpha & \cos 2\alpha \end{bmatrix}$.

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$,then $A^2 = $

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