Hello,

Let $\displaystyle E$ a $\displaystyle K$-vector space $\displaystyle (\text{dim}(E){\color{red}\le}\infty)$ and $\displaystyle (u,v)\in L(E)^2$.

Prove that $\displaystyle Id_E-u\circ v$ invertible $\displaystyle \Longleftrightarrow$ $\displaystyle Id_E-v\circ u$ invertible.