Answer
See below
Work Step by Step
Let $\begin{array}{c}{\det (A)=\left[\begin{array}{ccc}
a & b \\c &d \end{array}\right] }\end{array}$ and $\det(A)=1$
We will assume the elementary matrix $E=\begin{bmatrix}
0 & 1 \\ 1 & 0
\end{bmatrix}$
If we let $A_1=AE=\begin{bmatrix}
a&b \\c&d
\end{bmatrix}\begin{bmatrix}
0 & 1 \\ 1 & 0
\end{bmatrix}=\begin{bmatrix}
b & a \\ c & d
\end{bmatrix}$ then we have $\det(A_1)=\begin{vmatrix}
0 & 1 \\ 1 & 0
\end{vmatrix}=0.0-1.1=-1$
According to propert P9, $\det(A_1)=\det(EA)=\det (E).\det(A)=1.(-1)=-1$
Find matrix $B$: $\begin{bmatrix}
b & a \\ c & d
\end{bmatrix}\approx \begin{bmatrix}
-b & -a \\ d & c
\end{bmatrix} \approx \begin{bmatrix}
-b & -a \\ d-4b & c-4a
\end{bmatrix}$
Consequently, $\det(B)=1$
