AP EAMCET · Maths · Determinants
If \(A(\theta)=\left[\begin{array}{cc}i \sin \theta & \cos \theta \\ \cos \theta & i \sin \theta\end{array}\right]\) is a matrix, where \(i=\sqrt{-1}\), then which of the following is not true
- A \(\operatorname{det} A(\pi+\theta)=\operatorname{det} A(-\theta)\)
- B \(\operatorname{det} A(-\theta)=\operatorname{det} A(\theta)\)
- C \(\operatorname{det}[A(\theta)]^{-1}=1\)
- D \(\operatorname{det} A(-\theta)=-1\)
Answer & Solution
Correct Answer
(C) \(\operatorname{det}[A(\theta)]^{-1}=1\)
Step-by-step Solution
Detailed explanation
\(A(\theta)=\left[\begin{array}{cc}i \sin \theta & \cos \theta \\ \cos \theta & i \sin \theta\end{array}\right]\) where \(i=\sqrt{-1}\) \(\therefore|A(\theta)|=i^2 \sin ^2 \theta-\cos ^2 \theta\) \(=-\left(\sin ^2 \theta+\cos ^2 \theta\right)=-1\)…
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