Ononot — Let A and B be two n \times n matrices that commute (AB = BA

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Eigenvalues & Eigenvectorsmedium

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Let $A$ and $B$ be two $n \times n$ matrices that commute ( $AB = BA$ ). If $v$ is an eigenvector of $A$ with eigenvalue $\lambda$ , and the eigenspace $E_\lambda$ of $A$ has dimension 1, which of the following is true?