A) \[4A-3I\]
B) \[3A-AI\]
C) \[A-I\]
D) \[A+I\]
Correct Answer: A
Solution :
\[{{A}^{2}}=A\,.\,A=\left[ \begin{matrix} \text{2} & -1 \\ -1 & 2 \\ \end{matrix} \right]\,\left[ \begin{matrix} \text{2} & -1 \\ -1 & 2 \\ \end{matrix} \right]=\left[ \begin{matrix} \text{5} & -4 \\ -4 & 5 \\ \end{matrix} \right]\] Þ \[4A-3I=\,\left[ \begin{matrix} \text{8} & -4 \\ -4 & 8 \\ \end{matrix} \right]\,-\,\left[ \begin{matrix} \text{3} & 0 \\ 0 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 5 & -4 \\ -4 & 5 \\ \end{matrix} \right]\].
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