Ononot — Let V be the vector space of 2 \times 2 matrices. Define the

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Eigenvalues & Eigenvectorshard

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Let $V$ be the vector space of $2 \times 2$ matrices. Define the linear transformation $T: V \to V$ by $T(M) = AM - MA$ where $A = \begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}$ . What are the eigenvalues of $T$ ?