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

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Vectors & Spaceshard

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Let $V$ be the vector space of $2 \times 2$ matrices. Consider the linear operator $T: V \to V$ defined by $T(A) = MA - AM$ , where $M = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}$ . What is the rank of $T$ ?