More identities for Fibonacci and Lucas quaternions

In this paper, we define the associate matrix as%

Keywords:

Fibonacci Quaternions, Lucas Quaternions recurrence relations,

Koshy, T. Fibonacci and Lucas numbers with applications, Wiley, Newyork, 2001.
Horadam, A. F. Complex Fibonacci numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
Iyer, M. R. A note on Fibonacci Quaternions, The Fib. Quarterly, 3 (1969), 225-229.
Swamy, M. N. S. On generalized Fibonacci quaternions, The Fib. Quarterly, 5 (1973), 547-550.
Halıcı, S. On Fibonacci Quaterions, Adv. Appl. Clifford Algebras, 12 (2012), 321-327.
Akyiğit, M., Kösal, H. H., Tosun, M. Split Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 535-545.
Akyiğit, M., Kösal, H. H., Tosun, M. Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24 (2014), 631-641.
Tan, E., Yılmaz, S., Şahin, M. A new generalization of Fibonacci quaternions, Chaos Solitions Fractals, 82 2016, 1-4.
Tan, E., Yılmaz, S., Şahin, M. A Note on bi-periodic Fibonacci and Lucas quaternions, Chaos Solitions Fractals, 85 2016, 138-142.
Tan, E., Sahin, M., Yilmaz, S. The generalized bi-periodic Fibonacci quaternions and octonions. Novi Sad J. Math. doi.org/10.30755/NSJOM.07284.
Morais, J. P., Georgiev, S., Spröbig, W. Real Quaternionic Calculus Handbook, Birkhauser, London, 2014.