Consider a matrix \( A=[a i j] \) of order \( 3 \times 3 \) such that aij \( =(k)^{i+j} \) where....

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Consider a matrix \( A=[a i j] \) of order \( 3 \times 3 \) such that aij \( =(k)^{i+j} \) where \( k \in I \). Match the following lists:
\( \mathrm{P} \)
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ List-I } & & \multicolumn{1}{|c|}{ List-II } \\
\hline (A) & \( A \) is singular if & (P) & \( k \in\{0\} \) \\
\hline (B) & \( A \) is null matrix if & (Q) & \( k \in \phi \) \\
\hline (C) & \begin{tabular}{l}
\( A \) is skew-symmetric \\
which is not null matrix \\
if
\end{tabular} & (R) & \( k \in \mathrm{I} \) \\
\hline (D) & \( A^{2}=3 A \) if & (S) & \( k \in\{-1,0,1\} \) \\
\hline
\end{tabular}
A
(1) \( \mathrm{R} \)
(2) \( \mathrm{S} \)
(3) \( \mathrm{R} \)
(4) Q
B
\( \mathrm{P} \)
\( P \)
\( \mathrm{P} \)
\( \mathrm{P} \)
C
\( \mathrm{S} \)
Q
Q
\( \mathrm{R} \)
D
Q
\( \mathrm{R} \)
S
S


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