A) 5
B) 25
C) -5
D) -25
Correct Answer: B
Solution :
\[B\ne O\] \ \[{{A}^{2}}=\left[ \begin{matrix} 1 & 3 \\ 2 & 1 \\ \end{matrix} \right]\,\left[ \begin{matrix} 1 & 3 \\ 2 & 1 \\ \end{matrix} \right]\,=\,\left[ \begin{matrix} 7 & 6 \\ 4 & 7 \\ \end{matrix} \right]\] and\[{{A}^{2}}-2A=\left[ \begin{matrix} 5 & 0 \\ 0 & 5 \\ \end{matrix} \right]\,,\text{det }({{A}^{2}}-2A)=\left| \,\begin{matrix} 5 & 0 \\ 0 & 5 \\ \end{matrix}\, \right|=25\].
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