A=\left(
\begin{array}{ccc}
 2 & 1 & a \\
 3 & 5 & 0 \\
 1 & 4 & 1
\end{array}
\right)\sim \left(
\begin{array}{ccc}
 1 & 4 & 1 \\
 3 & 5 & 0 \\
 2 & 1 & a
\end{array}
\right)
\begin{array}{c}
 
\begin{array}{c}
 I(-3)+\text{II} \\
 \sim 
\end{array}
 \\
 I(-2)+\text{III}
\end{array}
\left(
\begin{array}{ccc}
 1 & 4 & 1 \\
 0 & -7 & -3 \\
 0 & -7 & a-2
\end{array}
\right)
\begin{array}{c}
 
\begin{array}{c}
 \text{II}(-1)+\text{III} \\
 \sim 
\end{array}
 \\
 \square 
\end{array}
\left(
\begin{array}{ccc}
 1 & 4 & 1 \\
 0 & -7 & -3 \\
 0 & 0 & a+1
\end{array}
\right).