AP EAMCET · Maths · Matrices
Let \(A=\left(\begin{array}{ll}-\cot \theta & \operatorname{cosec} \theta \\ \operatorname{cosec} \theta & -\cot \theta\end{array}\right)\). If \(A^{-1}=A\) at \(\theta=\theta_1\) and \(A^{-1}\) \(+\mathrm{A}=\mathrm{O}\) at \(\theta=\theta_2\), then which one of the following is True?
- A \(\theta_1=\frac{\pi}{2}, \theta_2=\pi\)
- B \(\theta_1=\frac{\pi}{2}\), such \(\theta_2\) does not exist
- C \(\theta_1=\frac{\pi}{4}, \theta_2=\frac{\pi}{2}\)
- D such \(\theta_1\) does not exist, \(\theta_2=\pi\)
Answer & Solution
Correct Answer
(C) \(\theta_1=\frac{\pi}{4}, \theta_2=\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Given \(A=\left(\begin{array}{ll}-\cot \theta & \operatorname{cosec} \theta \\ \operatorname{cosec} \theta & -\cot \theta\end{array}\right)\) Now \(|A|=\cot ^2 \theta-\operatorname{cosec}^2 \theta=-1\) and…
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