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RREF of $$$\left[\begin{array}{cc}i & 1\\-1 & i\end{array}\right]$$$
Related calculators: Gauss-Jordan Elimination Calculator, Matrix Inverse Calculator
Your Input
Find the reduced row echelon form of $$$\left[\begin{array}{cc}i & 1\\-1 & i\end{array}\right]$$$.
Solution
Divide row $$$1$$$ by $$$i$$$: $$$R_{1} = - i R_{1}$$$.
$$$\left[\begin{array}{cc}1 & - i\\-1 & i\end{array}\right]$$$
Add row $$$1$$$ to row $$$2$$$: $$$R_{2} = R_{2} + R_{1}$$$.
$$$\left[\begin{array}{cc}1 & - i\\0 & 0\end{array}\right]$$$
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.
Answer
The reduced row echelon form is $$$\left[\begin{array}{cc}1 & - i\\0 & 0\end{array}\right]$$$A.