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If \(A=\frac{1}{2}\left[\begin{array}{cc}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{array}\right]\), then: [JEE Main 2023…

Q1

If \(A=\frac{1}{2}\left[\begin{array}{cc}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{array}\right]\), then:

[JEE Main 2023, 1 Feb (Shift 2)]

a

\(A^{30}-A^{25}=2 I\)

b

\(A^{30}+A^{25}+A=I\)

c

\(A^{30}+A^{25}-A=I\)

d

\(A^{30}=A^{25}\)

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