grandes-ecoles 2010 QIIF3

grandes-ecoles · France · centrale-maths2__pc Matrices Linear Transformation and Endomorphism Properties

Let $A , B$ and $M$ be three elements of $\mathcal { M } _ { 0 } ( 2 , \mathbb { K } )$. We assume that the matrices $A$ and $[ A , B ]$ commute.
Prove that the matrix $[ A , B ]$ is nilpotent.

Let $A , B$ and $M$ be three elements of $\mathcal { M } _ { 0 } ( 2 , \mathbb { K } )$. We assume that the matrices $A$ and $[ A , B ]$ commute.

Prove that the matrix $[ A , B ]$ is nilpotent.

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