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If A = $A = [\begin{matrix} i & - i \\ - i & i \end{matrix}] a n d B = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]$ the A⁸ equals

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64 B

-64 B

-128 B

128 B

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detailed solution

Correct option is D

We have, A=i-i-ii=i 1-1-11= i B⇒A2=(iB)2=i2B2=-B2=-1-1-111-1-11=-222-2=-2B⇒ A4 = (–2B)2 = 4B2 = 4(2B) = 8B⇒ A8 = (A4)2 = (8B)2 = 64B2 = 128B

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If A = A=i-i-ii and B=1-1-11 the A8 equals

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Ready to Test Your Skills?

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If A = $A = [\begin{matrix} i & - i \\ - i & i \end{matrix}] a n d B = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]$ the A⁸ equals