I am given 2 linear maps: $T,S$, both from $V$ to $V$, satisfying $T^2 = S^2$.
$T,S \ne id$, and $T,S \ne 0$.
The question given is: Does it necessarily mean that $T=S$ or $T=-S$? (or not both?). Prove!
I think that this is not necessarily true, but I can't find a counterexample to support my claim.
Any ideas? thanks.