Which of the following matrices are orthogonal (ATA=IA^T A = IATA=I)?
(0110)\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}(0110)
(cosθ−sinθsinθcosθ)\begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}(cosθsinθ−sinθcosθ)
(1000)\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}(1000)
(1212−1212)\begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{pmatrix}(21−212121)