# Swapping matrix rows with basic row operations

The basic row operations on a matrix include adding a multiple of one row to another row and multiplying a row by a nonzero number.

How can I use a sequence of just these operations to swap the rows of this matrix like so:

$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ $\to \begin{pmatrix} c & d \\ a & b \end{pmatrix}$

Thanks for the hint.

• Row-swapping is usually included as another row-operation – Omnomnomnom Aug 10 '15 at 17:08