Given, $\quad A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0\end{array}\right]$
$\therefore A^2-2 A=\left[\begin{array}{lll}
1 & 1 & 1 \\
0 & 2 & 1 \\
0 & 1 & 1
\end{array}\right]-\left[\begin{array}{lll}
2 & 0 & 2 \\
0 & 2 & 2 \\
0 & 2 & 0
\end{array}\right]$


$\begin{aligned}
\text { Now, }|A| & =1(0-1)-0+1(0)=-1 \\
C_{11} & =-1, C_{12}=0, C_{13}=0 \\
C_{21} & =-(-1)=1, C_{22}=0, C_{23}=-1 \\
C_{31} & =-1, C_{32}=-(1), C_{33}=1 \\
\therefore \quad A^{-1} & =-1\left[\begin{array}{rrr}
-1 & 1 & -1 \\
0 & 0 & -1 \\
0 & -1 & 1
\end{array}\right]
\end{aligned}$
$\therefore$ From Eq. (i)
$A^2-2 A=-A^{-1}$