Nilpotent mapping/Commute/Nilpotent/Exercise

Let ${}V$ be a ${}K$-vector space, and let

$\varphi \colon V\longrightarrow V$

denote a nilpotent linear mapping. Let

$\psi \colon V\longrightarrow V$

be another linear mapping satisfying

${}\psi \circ \varphi =\varphi \circ \psi \,.$

Show that ${}\psi \circ \varphi$ is also nilpotent.

Create a solution