JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A =\frac{1}{2}\left[\begin{array}{cc}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{array}\right]\), then :
- A \(A ^{30}- A ^{25}=2 I\)
- B \(A ^{30}+ A ^{25}+ A = I\)
- C \(A ^{30}+ A ^{25}- A = I\)
- D \(A ^{30}= A ^{25}\)
Answer & Solution
Correct Answer
(C) \(A ^{30}+ A ^{25}- A = I\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} A =\frac{1}{2}\left[\begin{array}{cc}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{array}\right] \\ A =\left[\begin{array}{cc}\cos 60^{\circ} & \sin 60^{\circ} \\ -\sin 60^{\circ} & \cos 60^{\circ}\end{array}\right]\end{array}\)…
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