Question

Find the inverse of this simple 2x2 matrix:

Answer 1

\[\left[\begin{matrix}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{matrix}\right]\]

Answer 2

The inverse of the matrix
\[A=\left[\begin{matrix}a & b \\ c& d\end{matrix}\right]\]
is

\[A ^{-1}= \frac{ 1 }{ (ad-bc) }\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

Answer 3

Verification,
\[A*A ^{-1}= I\]

where

\[I=\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]