[tag:duplicate] These two posts are about the same identity and they are both asking for a proof by induction:
[Induction proof on Fibonacci sequence: $F(n-1) \cdot F(n+1) - F(n)^2 = (-1)^n$](http://math.stackexchange.com/questions/523925/),
[Induction proof $F(n)^2 = F(n-1)F(n+1)+(-1)^{n-1}$ for n $\ge$ 2 where n is the Fibonacci sequence](http://math.stackexchange.com/questions/783152/). One of them contains an attempt by the OP, otherwise they seem the same to me. (There is also at least one another post about the same identity. But as these posts are specifically about inductive proof, …