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Mathematics Question on Matrices

If A=[cos⁡αsin⁡α −sin⁡αcos⁡α]A = \begin{bmatrix}\cos\alpha&\sin\alpha\\\ - \sin\alpha&\cos\alpha\end{bmatrix} , then AA′=AA' =

A

A

B

Zero matrix

C

A'

D

I

Answer

I

Explanation

Solution

AA′=[cos⁡αsin⁡α −sin⁡αcos⁡α][cos⁡α−sin⁡α sin⁡αcos⁡α]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}
=[10 01]=I= \begin{bmatrix} 1 &0\\\ 0 & 1 \end{bmatrix} = I