Brahmagupta-Fibonacci Identity/Proof 3

Proof
Lagrange's Identity gives:
 * $\displaystyle \left({\sum_{k \mathop = 1}^n {a_k}^2}\right) \left({\sum_{k \mathop = 1}^n {b_k}^2}\right) - \left({\sum_{k \mathop = 1}^n a_k b_k}\right)^2 = \sum_{i \mathop = 1}^{n - 1} \sum_{j \mathop = i + 1}^n \left({a_i b_j - a_j b_i}\right)^2$

Setting $n = 2$: