Let f(x)=αx(x+1),x≠−1. Then for what value of α is f(f(x))=x?

f(x)=αxx+1,x≠−1  f(f(x))=x or α∞xx+1αxx+1+1=x  or α2x(α+1)x+1=x  or  (α+1)x2+1−α2x=0  or  α+1=0 and 1−α2=0 [As it is true ∀x≠−1 , Eq. (1) is an identity]  or  α=−1