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If $A=\left(\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right), B=\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right), C=\left(\begin{array}{ll}0 & i \\ i & 0\end{array}\right)$
where $i=\sqrt{-1}$, then which one of the following is correct?
Options:
where $i=\sqrt{-1}$, then which one of the following is correct?
Solution:
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Verified Answer
The correct answer is:
$A B=-C$
$\mathrm{AB}=\left(\begin{array}{cc}\mathrm{i} & 0 \\ 0 & -1\end{array}\right)\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right)=\left(\begin{array}{cc}0 & -1 \\ -\mathrm{i} & 0\end{array}\right)$
$\mathrm{AB}=-\left(\begin{array}{ll}0 & \mathrm{i} \\ \mathrm{i} & 0\end{array}\right)=-\mathrm{C}$
$\mathrm{AB}=-\left(\begin{array}{ll}0 & \mathrm{i} \\ \mathrm{i} & 0\end{array}\right)=-\mathrm{C}$
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