# [高等代数] 请教北大直博高代一题

 若$A\in Mn(\mathbb{C})$是$n$阶幂零矩阵,定义线性变换$$T_A:Mn(\mathbb{C})\rightarrow Mn(\mathbb{C});B\mapsto AB-BA;\forall B\in Mn(\mathbb{C})$$ 若矩阵$B$满足条件$(T_A)^2 (B)=0$,证明:矩阵$AB$为幂零矩阵。

 This is a result called Jacobson's Lemma, first proven in the paper "Rational Methods in the Theory of Lie Algebras" by Nathan Jacobson.

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