Match the following lists: \begin{tabular}{|c|c|c|c|} \hline & List-I & & List-II \\ \hline A. &....

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Match the following lists:
\begin{tabular}{|c|c|c|c|}
\hline & List-I & & List-II \\
\hline A. & \begin{tabular}{l}
\( (I-A)^{n} \) is, if \( A \) is \\
idempotent
\end{tabular} & P. & \( 2^{\mathrm{n}-1}(I-A) \) \\
\hline B. & \begin{tabular}{l}
\( (I-A)^{n} \) is, if \( A \) is \\
involuntary
\end{tabular} & Q. & \( I-n A \) \\
\hline C. & \begin{tabular}{l}
\( (I-A)^{n} \) is, if \( A \) is \\
nilpotent of index 2.
\end{tabular} & R. & \( A \) \\
\hline D. & \begin{tabular}{l}
If \( A \) is orthogonal, then \\
\( \left(A^{T}\right)^{-1} \)
\end{tabular} & S. & \( I-A \) \\
\hline & \( \mathbf{B} \) & D & \\
\hline (1) & Q & S & \\
\hline (2) & \( \mathrm{P} \) & \( \mathrm{R} \) & \\
\hline (3) & S & Q & \\
\hline (4) & \( P \) & \( \mathrm{R} \) & \\
\hline
\end{tabular}


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