Answer
$\begin{bmatrix}
1 &-2\\
0 & 1
\end{bmatrix}$
Work Step by Step
We can reduce A to row-echelon form using the following sequence of elementary row operations:
$\begin{bmatrix}
3 & 5\\
1& -2
\end{bmatrix} \approx^1 \begin{bmatrix}
1& -2\\
3 & 5
\end{bmatrix}\approx^2 \begin{bmatrix}
1& -2\\
0&11
\end{bmatrix}\approx^3 \begin{bmatrix}
1 & -2\\
0& 1
\end{bmatrix}$
$1. P_{12}$
$2.A_{12}(-3)$
$3.M_2( \frac{1}{11})$
So, elementary matrices are $M_2( \frac{1}{11}),A_{12}(-3),P_{12}=\begin{bmatrix}
1 &-2\\
0 & 1
\end{bmatrix}$
