If $A = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix}$, then :
Answer & explanation
Correct answer: option 1
$A = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix}$
$A' = \begin{bmatrix} \cos α & -\sin α\\ \sin α & \cos α \end{bmatrix}$
So $AA' = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix} \begin{bmatrix} \cos α & -\sin α\\ \sin α & \cos α \end{bmatrix}$
$AA' = \begin{bmatrix} \cos^2 α + \sin^2 α & -\cos α \sin α + \cos α \sin α\\ -\cos α \sin α + \cos α \sin α & \cos^2α + \sin^2α \end{bmatrix}$
$= \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix} = I$