If $ \mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & -\mathrm{i} \ -\mathrm{i} & \mathrm{i}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & -1 \ -1 & 1\end{array}\right] $, then $ \mathrm{A}^{8} $ equals

Question

If $ \mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & -\mathrm{i} \ -\mathrm{i} & \mathrm{i}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & -1 \ -1 & 1\end{array}\right] $, then $ \mathrm{A}^{8} $ equals, $ 4 \mathrm{~B} $, 128B, $ -128 \mathrm{~B} $, $ -64 \mathrm{~B} $

MARKS App · Accepted Answer

We have A = i B ⇒ A 2 = i B 2 = i 2 B 2 = - B 2 = 2 - 2 - 2 2 = - 2 B ⇒ A 4 = - 2 B 2 = 4 B 2 = 4 2 B = 8 B ⇒ A 8 = A 4 2 = 8 B 2 = 64 B 2 = 128 B

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