\left(A\left|A_p\right.\right)=\left(
\begin{array}{ccccc}
 a & 1 & 1 & | & 0 \\
 1 & a & 1 & | & 2 \\
 1 & 1 & a & | & a
\end{array}
\right)
\begin{array}{c}
 I_v\longleftrightarrow \text{III}_v \\
 
\begin{array}{c}
 \sim  \\
 \square 
\end{array}

\end{array}
\left(
\begin{array}{ccccc}
 1 & 1 & a & | & a \\
 1 & a & 1 & | & 2 \\
 a & 1 & 1 & | & 0
\end{array}
\right)
\begin{array}{c}
 I_v(-1)+\text{II}_v \\
 
\begin{array}{c}
 \sim  \\
 I_v(-a)+\text{II}_v
\end{array}

\end{array}
\left(
\begin{array}{ccccc}
 1 & 1 & a & | & a \\
 0 & a-1 & 1-a & | & 2-a \\
 0 & 1-a & 1-a^2 & | & -a^2
\end{array}
\right)
\begin{array}{c}
 \text{II}_v+\text{III}_v \\
 
\begin{array}{c}
 \sim  \\
 \square 
\end{array}

\end{array}