If A=(cosθ−sinθsinθcosθ)A = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}A=(cosθsinθ−sinθcosθ), what is ATA^TAT?
(cosθ−sinθsinθcosθ)\begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}(cosθsinθ−sinθcosθ)
(cosθsinθ−sinθcosθ)\begin{pmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{pmatrix}(cosθ−sinθsinθcosθ)
(−cosθsinθ−sinθ−cosθ)\begin{pmatrix} -\cos \theta & \sin \theta \\ -\sin \theta & -\cos \theta \end{pmatrix}(−cosθ−sinθsinθ−cosθ)
(sinθcosθcosθ−sinθ)\begin{pmatrix} \sin \theta & \cos \theta \\ \cos \theta & -\sin \theta \end{pmatrix}(sinθcosθcosθ−sinθ)