Permutation Matrices

Permutation matrices change the positions of rows or columns in a Matrix that it is multiplying. Depending on where the Permutation Matrix $P$ is located with respect to $A$, it will either swap rows ($P$ left of $A$) or columns ($P$ right of $A$).

$$\underset{\text{Exchange Rows}}{\underbrace{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}}\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\underset{\text{Exchange Columns}}{\underbrace{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}}$$