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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.

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    $\begingroup$ Row-swapping is usually included as another row-operation $\endgroup$ – Omnomnomnom Aug 10 '15 at 17:08
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Hint: add -1 times row 1 to row 2, then add row 2 to row 1. Can u take it from here?

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