grandes-ecoles 2022 Q8

grandes-ecoles · France · centrale-maths1__psi Matrices Matrix Algebra and Product Properties
Suppose that $M , N$ and $M + N$ are nilpotent. By computing $( M + N ) ^ { 2 } - M ^ { 2 } - N ^ { 2 }$, show that $\operatorname { tr } ( M N ) = 0$. 
Suppose that $M , N$ and $M + N$ are nilpotent. By computing $( M + N ) ^ { 2 } - M ^ { 2 } - N ^ { 2 }$, show that $\operatorname { tr } ( M N ) = 0$.
Paper Questions
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