Linear Algebra - Eigenvalues and Eigenvectors

Suppose $\lambda$ is an eigenvalue of matrix A and x is the corresponding eigenvector. Let x also be an eigenvector of the matrix B = A - 2I, where I is the identity matrix. Then, the eigenvalue of B corresponding to the...

For the matrix [A] = [1 2 3] [3 2 1] [3 1 2] which of the following statements is/are TRUE?

The smallest eigenvalue and the corresponding eigenvector of the matrix [[2, -2], [-1, 6]], respectively, are

The matrix $\begin{pmatrix} 2 & -4 \ 4 & -2 \ \end{pmatrix}$ has

Consider the matrix $\begin{bmatrix} 5 & -1 \ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?