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

Identity matrix

The correct answer is Option (4) → Identity matrix

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

$A^T=\begin{bmatrix} \cos\alpha & \sin \alpha \\-\sin \alpha & \cos\alpha \end{bmatrix}$

$AA^T=\begin{bmatrix} \cos^2\alpha+\sin^2\alpha&0 \\0&\cos^2\alpha+\sin^2\alpha \end{bmatrix}$

$=\begin{bmatrix} 1a & 0 \\0 & 1 \end{bmatrix}$  $[\sin^2\alpha+\cos^2\alpha=1]$