Mathematics - Matrices Question with Solution | TestHub

Here $|A-\lambda I|=0$

$\begin{array}{rl}& \left|\begin{array}{cc}1-\lambda & 0\\ -1& 7-\lambda \end{array}\right|=0\\ & \Rightarrow (1-\lambda )(7-\lambda )=0\\ & \Rightarrow {\lambda }^2-8\lambda +7=0\\ & \Rightarrow A^2-8A+7I_2=0\\ & \Rightarrow A^2=8A-7I_2\\ & \Rightarrow k=-7\\ & \Rightarrow |k|=7Ans\end{array}$