題組內容

5 Suppose that $A \in M_{n \times n}(\mathbb{R})$. Let $T : M_{n \times n}(\mathbb{R}) \to M_{n \times n}(\mathbb{R})$ be defined by T(X) = AX - XA.

b. (10) Let $A = \begin{bmatrix} 3 & 2 \\ 2 & 0 \end{bmatrix}$. Find the eigenvalues and eigenvectors of $T$.