A) \[-6\]
B) \[-5\]
C) \[-4\]
D) \[4\]
E) \[6\]
Correct Answer: A
Solution :
Given, \[A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\] \[\Rightarrow \] \[|A|=5-6=-1\] \[\therefore \] \[|{{A}^{200-}}-5{{A}^{2008}}|=|{{A}^{2008}}||A-5I|\] \[={{(-1)}^{2008}}\left| \left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]-\left[ \begin{matrix} 5 & 0 \\ 0 & 5 \\ \end{matrix} \right] \right|\] \[=\left| \begin{matrix} -4 & 2 \\ 3 & 0 \\ \end{matrix} \right|\]
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