\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that for every \(\theta \in \mathbb{R}\), the rotation matrix \(R_\theta = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}\) is invertible, and compute \(R_\theta^{-1}\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.