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  4. If A = [ cosα& sinα - sinα& cosα] , then AA' =

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Q. If $A = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix}$ , then $AA' = $

KCETKCET 2018

Solution:

$AA' = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix} \begin{bmatrix}\cos\alpha&-\sin\alpha\\ \sin\alpha&\cos\alpha\end{bmatrix}$
$ = \begin{bmatrix} 1 &0\\ 0 & 1 \end{bmatrix} = I $