RREF of $$$\left[\begin{array}{ccc}1 & -1 & -1\\2 & -2 & 1\end{array}\right]$$$

Find the reduced row echelon form of $$$\left[\begin{array}{ccc}1 & -1 & -1\\2 & -2 & 1\end{array}\right]$$$.

Subtract row $$$1$$$ multiplied by $$$2$$$ from row $$$2$$$: $$$R_{2} = R_{2} - 2 R_{1}$$$.

$$$\left[\begin{array}{ccc}1 & -1 & -1\\0 & 0 & 3\end{array}\right]$$$

Since the element at row $$$2$$$ and column $$$2$$$ (pivot element) equals $$$0$$$, we need to swap the rows.

Find the first nonzero element in column $$$2$$$ under the pivot entry.

As can be seen, there are no such entries. Move to the next column.

Divide row $$$2$$$ by $$$3$$$: $$$R_{2} = \frac{R_{2}}{3}$$$.

$$$\left[\begin{array}{ccc}1 & -1 & -1\\0 & 0 & 1\end{array}\right]$$$

Add row $$$2$$$ to row $$$1$$$: $$$R_{1} = R_{1} + R_{2}$$$.

$$$\left[\begin{array}{ccc}1 & -1 & 0\\0 & 0 & 1\end{array}\right]$$$

The reduced row echelon form is $$$\left[\begin{array}{ccc}1 & -1 & 0\\0 & 0 & 1\end{array}\right]$$$A.