More fun in 2015, Part 15

Algebra Level 2

$\large \begin{cases} {a_n=a_{n-1}a_{n-2}-b_{n-1}b_{n-2} } \\ { b_n=b_{n-1}a_{n-2}+a_{n-1}b_{n-2} } \end{cases}$

Two sequences $a_n$ and $b_n$ begin with values $a_1=b_1=a_2=b_2=1$ and satisfy the recursive relations above for $n>2$ .