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If $A = (\begin{array}{cc} i & - i \\ - i & i \end{array})$ and $B = (\begin{array}{cc} 1 & - 1 \\ - 1 & 1 \end{array})$ , then $A^{8}$ equals

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128 B

32 B

16 B

64 B

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detailed solution

Correct option is A

A=iB⇒A2=i2B2=(−1)1−1−111−1−11=−2B⇒A4=(−2B)2=4B2=4(2B)=8B⇒A8=(8B)2=64B2=64(2B)=128B

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If A=i−i−ii and B=1−1−11, then A8 equals

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If $A = (\begin{array}{cc} i & - i \\ - i & i \end{array})$ and $B = (\begin{array}{cc} 1 & - 1 \\ - 1 & 1 \end{array})$ , then $A^{8}$ equals