Proving that $h$ is an automorphism if $2h^2+4h+2I=0$ I dont know how i can solve this problem. You have one vector space $V$ with a linear transformation: $h: V \to  V$. So we have an endomorphism.  The question is to show that if $h$ satisfies $2h^2+4h+2I=0$, where I is the identity transformation and 0 is the null transformation, then $h$ is an automorphism. Why? Please help, thanks.

Hint.
If $2 h^2 + 4h +2I=0$ then $h(-h-2h)=I$
