Let \(A = \begin{bmatrix} 1 & 1 \\ 2 & 1\end{bmatrix}\). You are given that \(A \stackrel{R_2 \leftarrow R_2 - 2R_1}{\longrightarrow} \begin{bmatrix} 1 & 1 \\ 0 & -1\end{bmatrix} \stackrel{R_1 \leftarrow R_1 + R_2}{\longrightarrow} \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix} \stackrel{R_2 \leftarrow -R_2}{\longrightarrow} \begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}. \)
Which of the following equals \(A\)?
\(\begin{bmatrix} 1 & 0 \\ -2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \)
\(\begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \)
\(\begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & -1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \)