A) \[\left[ \begin{matrix} 3n & -4n \\ n & -n \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2+n & 5-n \\ n & -n \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} {{3}^{n}} & {{(-4)}^{n}} \\ {{1}^{n}} & {{(-1)}^{n}} \\ \end{matrix} \right]\]
D) None of these
Correct Answer: D
Solution :
\[X=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right]\Rightarrow {{X}^{2}}=\left[ \begin{matrix} 5 & -8 \\ 2 & -3 \\ \end{matrix} \right]\]. Clearly for\[n=2\], the matrices in (a), (b), (c) do not tally with\[\left[ \begin{matrix} 5 & -8 \\ 2 & -3 \\ \end{matrix} \right]\].
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