Find the inverse of the following matrix. $\left[ \begin{array} { c c }
\cos \theta & \sin \theta \
- \sin \theta & \cos \theta
\end{array} \right]$
A) $\left[ \begin{array} { c c }
\cos \theta & - \sin \theta \
\sin \theta & \cos \theta
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- \cos \theta & - \sin \theta \
\sin \theta & \cos \theta
\end{array} \right]$
C) $\left[ \begin{array} { c c }
\cos \theta & \sin \theta \
- \sin \theta & \cos \theta
\end{array} \right]$
D) $\left[ \begin{array} { c c }
\cos \theta & \sin \theta \
- \sin \theta & - \cos \theta
\end{array} \right]$
E) $\left[ \begin{array} { l l }
\cos \theta & - \sin \theta \
\sin \theta & - \cos \theta
\end{array} \right]$

Question

Find the inverse of the following matrix.   $\left[ \begin{array} { c c } 
\cos \theta & \sin \theta \
- \sin \theta & \cos \theta
\end{array} \right]$  
A)  $\left[ \begin{array} { c c } 
\cos \theta & - \sin \theta \
\sin \theta & \cos \theta
\end{array} \right]$
B)  $\left[ \begin{array} { c c } 
- \cos \theta & - \sin \theta \
\sin \theta & \cos \theta
\end{array} \right]$
C)  $\left[ \begin{array} { c c } 
\cos \theta & \sin \theta \
- \sin \theta & \cos \theta
\end{array} \right]$
D)  $\left[ \begin{array} { c c } 
\cos \theta & \sin \theta \
- \sin \theta & - \cos \theta
\end{array} \right]$
E)  $\left[ \begin{array} { l l } 
\cos \theta & - \sin \theta \
\sin \theta & - \cos \theta
\end{array} \right]$

Quizplus · Accepted Answer

The given matrix is a rotation matrix, and its inverse is the rotation in the opposite direction, which is achieved by changing the sign of the sine components, thus matching option A.

Find the Inverse of the Following Matrix [cos⁡θsin⁡θ−sin⁡θcos⁡θ]\left[ \begin{array} { c c } \cos \theta & \sin \theta \\- \sin \theta & \cos \theta\end{array} \right][cosθ−sinθ​sinθcosθ​]

Find the Inverse of the Following Matrix $\left[ \begin{array} { c c } \cos \theta & \sin \theta \\- \sin \theta & \cos \theta\end{array} \right]$