The answer is “No”. Adding \(-2\) times row 1 of the matrix \([A \mid I]\) to row 2 gives \(\begin{bmatrix} 1 & 2 & 1 & 0\\ 0 & 0 & -2 & 1\end{bmatrix}\). Since the matrix is in reduced row-echelon form and the first two columns do not give the identity matrix, \(A\) has no inverse.