grandes-ecoles 2010 QIIF2

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

Let $A , B$ and $M$ be three elements of $\mathcal { M } _ { 0 } ( 2 , \mathbb { K } )$.
Prove that the matrix $M$ is nilpotent if and only if the trace of the matrix $M ^ { 2 }$ is zero.

Let $A , B$ and $M$ be three elements of $\mathcal { M } _ { 0 } ( 2 , \mathbb { K } )$.

Prove that the matrix $M$ is nilpotent if and only if the trace of the matrix $M ^ { 2 }$ is zero.

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