If A=left[begin{array}{cc}0 & 1 1 & 0end{ar | vedclass

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(C) Given the matrix $ A = \left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array}ight] $.To find $ A^{2} $,we multiply the matrix $ A $ by itself:$ A^{2}

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$ \left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight] $

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(C) Given the matrix $ A = \left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array}ight] $.To find $ A^{2} $,we multiply the matrix $ A $ by itself:$ A^{2} = A \cdot A = \left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array}ight] \left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array}ight] $Performing matrix multiplication:$ A^{2} = \left[\begin{array}{ll} (0 	imes 0) + (1 	imes 1) & (0 	imes 1) + (1 	imes 0) \ (1 	imes 0) + (0 	imes 1) & (1 	imes 1) + (0 	imes 0) \end{array}ight] $$ A^{2} = \left[\begin{array}{ll} 0 + 1 & 0 + 0 \ 0 + 0 & 1 + 0 \end{array}ight] $$ A^{2} = \left[\begin{array}{ll} 1 & 0 \ 0 & 1 \end{array}ight] $This is the identity matrix $ I $ of order $ 2 	imes 2 $.

If $ A=\left[\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right] $,then $ A^{2} $ is equal to:

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