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 obtained by reversing the direction of rotation, which is achieved by changing the sign of the sine components, resulting in 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 $\left[ \begin{array} { c c } \cos \theta & \sin \theta \\- \sin \theta & \cos \theta\end{array} \right]$