Fibonacci related Proof

[psyclones]

Hi,

Can you give me any tips of how to begin this proof using the Fibonacci sequence?

F_n-1F_n+1 - F_n² = (-1)ⁿ , where Fibonacci numbers can be calculated by F_n = F_{n-1 +} F_n-2 

If I let n= k+1 then, but 

F_k F_k+2 - F_k+1² = (-1)^k+1

If k = 0 ,   0x1  - 1² =  -1  (true) , but how do I take it further. 

Edited March 11, 2018 by psyclones
found error in equ