Past exam of the options II course of the University of Oxford / 2012 / P / P3 / a

A real square matrix $Q$ is orthogonal when $Q^{T}Q=I$, equivalently $Q^{-1}=Q^T$. For $c=\cos \theta$ and $s=\sin \theta$,Thus $M(\theta )$ is orthogonal for every allowed angle, and indeed for every real angle.