Inverse matrix for a matrix with sinus and cosinus functions I have this matrix A:
$$\left(\begin{array}{cc} \cos x & -\sin x \\ \sin x & \cos x \end{array}\right)$$
and I need to create an inverse matrix for this matrix A. The sinus and cosinus functions in there makes me confused, I don't know how to start and proceed.
To count a determinant from this matrix is kinda easy, but how to count an inverse matrix to this?
Thank you

If $M$ is a matrix where
$$
M=\left(\begin{array}{cc} a & b \\ c & d \end{array}\right)
$$
then inverse of $M$  is
$$
M^{-1}=\frac{1}{ad-bc}\left(\begin{array}{cc} d & -b \\ -c & a \end{array}\right)
$$
Similarly
$$
A=\left(\begin{array}{cc} \cos x & -\sin x \\ \sin x & \cos x \end{array}\right)
$$
then inverse of $A$  is
\begin{align}
A^{-1}&=\frac{1}{(\cos x)(\cos x)-(-\sin x)(\sin x)}\left(\begin{array}{cc} \cos x & \sin x \\ -\sin x & \cos x \end{array}\right)\\
&=\frac{1}{\cos^2 x+\sin^2 x}\left(\begin{array}{cc} \cos x & \sin x \\ -\sin x & \cos x \end{array}\right)\\
&=\left(\begin{array}{cc} \cos x & \sin x \\ -\sin x & \cos x \end{array}\right)
\end{align}
where $\cos^2 x+\sin^2 x=1$.
