Question

If $I=\left\{\begin{array}{cc}1& 0\\ 0& 1\end{array}\right\},J=\left\{\begin{array}{cc}0& 1\\ -1& 0\end{array}\right\}$ and
$B=\left\{\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right\},thenB=$

• A. $I\cos \theta +J\sin \theta$
• B. $I\sin \theta +J\cos \theta$
• C. $I\cos \theta -J\sin \theta$
• D. $-I\cos \theta -J\sin \theta$

Answer 1

The correct option is A $I\cos \theta +J\sin \theta$

$B=\left\{\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right\}=cos\theta \left\{\begin{array}{cc}1& 0\\ 0& 1\end{array}\right\}+sin\theta \left\{\begin{array}{cc}0& 1\\ -1& 0\end{array}\right\}$
$=cos\theta I+sin\theta J$