Question:medium
Let \( A = \begin{bmatrix} 1 & \frac{-1-i\sqrt{3}}{2} \\ \frac{-1+i\sqrt{3}}{2} & 1 \end{bmatrix} \). Then \( A^{100} \) is equal to:
Let \( A = \begin{bmatrix} 1 & \frac{-1-i\sqrt{3}}{2} \\ \frac{-1+i\sqrt{3}}{2} & 1 \end{bmatrix} \). Then \( A^{100} \) is equal to:
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When you see the specific values $\frac{-1 \pm i\sqrt{3}}{2}$, immediately substitute $\omega$ and $\omega^2$. It transforms complex matrix multiplication into simple algebraic manipulation.
Updated On: May 2, 2026
- $2^{100} A$
- $2^{99} A$
- $2^{98} A$
- $A$
- $A^2$
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The Correct Option is B
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