iran-konkur 2013 Q140

iran-konkur · Other · konkur-riazi_1392 Matrices Linear System and Inverse Existence
140- If $A = \begin{bmatrix} 0 & -\tan\alpha \\ \tan\alpha & 0 \end{bmatrix}$ and $I$ is the identity matrix of order 2, the first row of $(I+A)(I-A)^{-1}$ is which of the following?
(1) $[\cos 2\alpha \;\; -\sin 2\alpha]$ (2) $[\cos 2\alpha \;\; \sin 2\alpha]$ (3) $[\sin 2\alpha \;\; \cos 2\alpha]$ (4) $[-\sin 2\alpha \;\; \cos 2\alpha]$
\textbf{140-} If $A = \begin{bmatrix} 0 & -\tan\alpha \\ \tan\alpha & 0 \end{bmatrix}$ and $I$ is the identity matrix of order 2, the first row of $(I+A)(I-A)^{-1}$ is which of the following?

(1) $[\cos 2\alpha \;\; -\sin 2\alpha]$ \qquad (2) $[\cos 2\alpha \;\; \sin 2\alpha]$ \qquad (3) $[\sin 2\alpha \;\; \cos 2\alpha]$ \qquad (4) $[-\sin 2\alpha \;\; \cos 2\alpha]$