If A= [ cc & - & ], then A^ 10 = - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A^{10}=$

A
$\left[\begin{array}{cc}\cos 10 \alpha & -\sin 10 \alpha \\ \sin 10 \alpha & \cos 10 \alpha\end{array}\right]$
✓
$\left[\begin{array}{cc}\cos 10 \alpha & \sin 10 \alpha \\ -\sin 10 \alpha & \cos 10 \alpha\end{array}\right]$
C
$\left[\begin{array}{cc}\cos 10 \alpha & \sin 10 \alpha \\ -\sin 10 \alpha & -\cos 10 \alpha\end{array}\right]$
D
$\left[\begin{array}{cc}\cos 10 \alpha & -\sin 10 \alpha \\ -\sin 10 \alpha & -\cos 10 \alpha\end{array}\right]$

✓

Answer

Correct option: B.

$\left[\begin{array}{cc}\cos 10 \alpha & \sin 10 \alpha \\ -\sin 10 \alpha & \cos 10 \alpha\end{array}\right]$

$\left[\begin{array}{cc}\cos 10 \alpha & \sin 10 \alpha \\ -\sin 10 \alpha & \cos 10 \alpha\end{array}\right]$

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