/sci/ - Science & Math

Is [math](f \circ g)^3 = I[/math] possible to prove?

[math](f \circ g)^2 = I[/math] is trivial, so [math](f \circ g)^3 = I[/math] reduces to proving [math]f \circ g = I[/math] or otherwise that [math]f = g[/math].

I feel like I'm missing a "trick" of some kind, please give me only a hint if possible.