A) \[-6\]
B) \[-5\]
C) \[-4\]
D) \[4\]
Correct Answer: A
Solution :
[a] Given, \[A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\] \[\Rightarrow \left| A \right|=5-6=-1\] \[\therefore \left| {{A}^{2009}}-5{{A}^{2008}} \right|=\left| {{A}^{2008}} \right|\left| A-5I \right|\] \[={{(-1)}^{2008}}\left| \left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]-\left[ \begin{matrix} 5 & 0 \\ 0 & 5 \\ \end{matrix} \right] \right|=\left| \begin{matrix} -4 & 2 \\ 3 & 0 \\ \end{matrix} \right|=-6\]
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