A) 3I
B) 5I
C) - 5I
D) None of these
Correct Answer: C
Solution :
\[{{A}^{2}}-6\,A=\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]\,\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]-6\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 19 & 6 \\ 18 & 7 \\ \end{matrix} \right]-\left[ \begin{matrix} 24 & 6 \\ 18 & 12 \\ \end{matrix} \right]\]\[\left[ \begin{matrix} -5 & 0 \\ 0 & -5 \\ \end{matrix} \right]=-5I\].
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