題組內容

4 Suppose that $A \in M{n \times k}(\mathbb{R})$ and $B \in M{m \times \ell}(\mathbb{R})$. Let $T: M{k \times m}(\mathbb{R}) \to M{n \times \ell}(\mathbb{R})$ be defined by $T(X) = AXB$.

b. (10) Let \( A = \left[ \begin{array}{ll}3 & 2\\ 2 & 0 \end{array} \right] \) and \( B = I_{2} \). Find the eigenvalues and eigenvectors of \( T \).