The given matrices are \[A=\begin{bmatrix}1&0&-2\\3&1&0\\1&0&-3\end{bmatrix},\ B=\begin{bmatrix}1&0&-3\\3&1&0\\1&0&-2\end{bmatrix}\]

Note that the matrix A can be obtained by interchanging the rows \(\displaystyle{R}_{{1}}\) and \(\displaystyle{R}_{{3}}\) of B.

Perform the same operation in \[I=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\] and obtain that \[R=\begin{bmatrix}0&0&1\\0&1&0\\1&0&0\end{bmatrix}\]

Check the condition as follows.

\[EA=\begin{bmatrix}0&0&1\\0&1&0\\1&0&0\end{bmatrix}\begin{bmatrix}1&0&-2\\3&1&0\\1&0&-3\end{bmatrix}\]

\[=\begin{bmatrix}1&0&-3\\3&1&0\\1&0&-2\end{bmatrix}\]

\(\displaystyle={B}\)

Thus , the required elementary matrix is \[E=\begin{bmatrix}0&0&1\\0&1&0\\1&0&0\end{bmatrix}\]