List of top General Aptitude Questions on Linear Algebra asked in GATE BM

Which one of the following vectors is an eigenvector corresponding to the eigenvalue \(\lambda = 1\) for the matrix \[ A = \begin{bmatrix} 1 & 1 & 0 \\ 1 & -1 & 0 \\ 1 & -1 & 1 \end{bmatrix}? \]