Chapter 2.4, Problem 12E

Finding an Elementary Matrix In Exercises $\mathit{ }9-12$, let $\mathit{ }\mathit{A}$, $\mathit{ }\mathit{B}$, and $\mathit{ }\mathit{C}$ be $\mathit{ }\mathit{A}=\left[\begin{array}{ccc}1& 2& -3\\ 0& 1& 2\\ -1& 2& 0\end{array}\right]$, $\mathit{ }\mathit{B}=\left[\begin{array}{ccc}-1& 2& 0\\ 0& 1& 2\\ 1& 2& -3\end{array}\right]$, and $\mathit{ }\mathit{C}=\left[\begin{array}{ccc}0& 4& -3\\ 0& 1& 2\\ -1& 2& 0\end{array}\right]$.

Find an elementary matrix $E$ such that $EC=A$.