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
Best Answer
HINT
Your matrix represents an anti-clockwise rotation about the origin, through $x$-radians.
Geometrically, what is the inverse of that transformation?
Clockwise rotations are given by negative angles.
If you insist upon findind the inverse algebraically, note that $\det = \cos^2x + \sin^2x \equiv 1$.