\begin{questions}
\item $A^2=\begin{pmatrix}2&1&1\\1&2&1\\1&1&2 \end{pmatrix}$.

$\begin{aligned}[t]
A+2I&=\begin{pmatrix}0&1&1\\1&0&1\\1&1&0\end{pmatrix}+\begin{pmatrix}2&0&0\\0&2&0\\0&0&2\end{pmatrix}\\
&=\begin{pmatrix}2&1&1\\1&2&1\\1&1&2 \end{pmatrix}\\
&=A^2.
\end{aligned}$

\item $\begin{aligned}[t]
A^3 &=A\times A^2\\
&=A\times(A+2I)\\
&=A^2+2AI\\
&=A+2I+2A\\
&= 3A + 2I.
\end{aligned}$
\end{questions}
