To find generalised eigenvector of a matrix

Question

The given matrix is A= $\begin{pmatrix} 2 & -1 \\ 1 & 4 \end{pmatrix}$. I needed to find generalised eigenvector. First I found that 3 is it's eigenvalue with algebraic multiplicity 2 but geometric multiplicity only 1 with eigenvector $(-1, 1)^T$. It was multiple choice question and I am confused about one point. Can there be two generalised eigenvectors? Because two options seems correct to me which are $(3, 2)^T$ and $(1, 0)^T$ because $(A-3I)^2\begin{pmatrix} 3 \\ 2 \end{pmatrix}=\begin{pmatrix} 0 \\ 0 \end{pmatrix}$ and $(A-3I)^2\begin{pmatrix} 1 \\ 0 \end{pmatrix}=\begin{pmatrix} 0 \\ 0 \end{pmatrix}$. So are these both options correct?