Linear Algebra - Eigenvalues and Eigenvectors

Consider the matrix $\begin{bmatrix} 1 & k \\ 2 & 1 \end{bmatrix}$, where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

Let the sets of eigenvalues and eigenvectors of a matrix B be {λk | 1 ≤ k ≤ n} and {vk | 1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where B = P⁻¹AP, r...