यदि A=left[begin{array}{cc}i & 0 0 & -iend{a | vedclass

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(A) दिए गए आव्यूह $A=\left[\begin{array}{cc}i & 0 \ 0 & -i\end{array}ight]$,$B=\left[\begin{array}{cc}0 & -1 \ 1 & 0\end{array}ight]$,और $C=\lef

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$A^2+B^2+C^2=3 A^2 B^2 C^2$

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(A) दिए गए आव्यूह $A=\left[\begin{array}{cc}i & 0 \ 0 & -i\end{array}ight]$,$B=\left[\begin{array}{cc}0 & -1 \ 1 & 0\end{array}ight]$,और $C=\left[\begin{array}{cc}0 & i \ i & 0\end{array}ight]$ हैं।आव्यूहों के वर्गों की गणना करने पर:$A^2 = \left[\begin{array}{cc}i & 0 \ 0 & -i\end{array}ight] \left[\begin{array}{cc}i & 0 \ 0 & -i\end{array}ight] = \left[\begin{array}{cc}i^2 & 0 \ 0 & (-i)^2\end{array}ight] = \left[\begin{array}{cc}-1 & 0 \ 0 & -1\end{array}ight] = -I$.$B^2 = \left[\begin{array}{cc}0 & -1 \ 1 & 0\end{array}ight] \left[\begin{array}{cc}0 & -1 \ 1 & 0\end{array}ight] = \left[\begin{array}{cc}-1 & 0 \ 0 & -1\end{array}ight] = -I$.$C^2 = \left[\begin{array}{cc}0 & i \ i & 0\end{array}ight] \left[\begin{array}{cc}0 & i \ i & 0\end{array}ight] = \left[\begin{array}{cc}i^2 & 0 \ 0 & i^2\end{array}ight] = \left[\begin{array}{cc}-1 & 0 \ 0 & -1\end{array}ight] = -I$.वर्गों का योग:$A^2+B^2+C^2 = (-I) + (-I) + (-I) = -3I = \left[\begin{array}{cc}-3 & 0 \ 0 & -3\end{array}ight]$.अब,$3 A^2 B^2 C^2$ की गणना करने पर:$3 A^2 B^2 C^2 = 3(-I)(-I)(-I) = 3(-I)^3 = 3(-I) = -3I$.चूंकि $A^2+B^2+C^2 = -3I$ और $3 A^2 B^2 C^2 = -3I$,इसलिए हम निष्कर्ष निकालते हैं कि $A^2+B^2+C^2 = 3 A^2 B^2 C^2$।

यदि $A=\left[\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right]$,$B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$ और $C=\left[\begin{array}{cc}0 & i \\ i & 0\end{array}\right]$ है,तो निम्नलिखित में से कौन सा सत्य है?

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