RREF of $$$\left[\begin{array}{cc}0 & 0\\0 & -1\end{array}\right]$$$

Find the reduced row echelon form of $$$\left[\begin{array}{cc}0 & 0\\0 & -1\end{array}\right]$$$.

Since the element at row $$$1$$$ and column $$$1$$$ (pivot element) equals $$$0$$$, we need to swap the rows.

Find the first nonzero element in column $$$1$$$ under the pivot entry.

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

Since the element at row $$$1$$$ 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.

The first nonzero element is at row $$$2$$$.

Swap the rows $$$1$$$ and $$$2$$$:

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

Multiply row $$$1$$$ by $$$-1$$$: $$$R_{1} = - R_{1}$$$.

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

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