TS EAMCET · Maths · Matrices
\(\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}\)
- A \(A(-\alpha, \beta)\)
- B \(A(-\alpha,-\beta)\)
- C \(A(\alpha,-\beta)\)
- D \(A(\alpha, \beta)\)
Answer & Solution
Correct Answer
(B) \(A(-\alpha,-\beta)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } A(\alpha, \beta)=\left[\begin{array}{rcc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \text { Now, }|A(\alpha, \beta)|=e^\beta\left(\cos ^2 \alpha+\sin ^2 \alpha\right)=e^\beta \\ &…
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