Answer
$$
\begin{bmatrix}
1 & 0 \\
0 & 1 \\
0 & 0 \\
\end{bmatrix}
$$
Work Step by Step
Given this matrix:
$$
\begin{bmatrix}
3 & 5 \\
5 & -2 \\
2 & 4 \\
\end{bmatrix}
$$
First, subtract the first row from the second:
$$
\begin{bmatrix}
3 & 5 \\
2 & -7 \\
2 & 4 \\
\end{bmatrix}
$$
Then third from the second, and vice versa, then cancel out the third row again, producing a matrix in row echelon form:
$$
\begin{bmatrix}
3 & 5 \\
0 & -11 \\
0 & 0 \\
\end{bmatrix}
$$
Lastly, divide the first and second rows by $3$ and $-11$ to make their leading coefficients $1$, and add $-5$ times the second row to the first row to yield a matrix in reduced row echelon form.
$$
\begin{bmatrix}
1 & 0 \\
0 & 1 \\
0 & 0 \\
\end{bmatrix}
$$
