Solution (source code)

= Solution

The <permutation matrix> is
$$
\boxed{E=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}.}
$$
Rows three and four of the <identity matrix> have been interchanged, so left multiplication interchanges those rows of any <matrix>.