Question

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

• A. A
• B. Zero matrix
• C. A'
• D. I

Answer 1

Answer: (D)

$A{A}^{\prime }=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{array}\right]\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]$
$=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=I$