Comment body goes here.
I’m pretty sure nobody knew that Fibonacci numbers occur in powers of a certain matrix without reading the hint. I certainly didn’t! So I doubt anyone would be able to solve this without the hints.
The 2x2 matrix used is:
[ 1 1 ]
[ 1 0 ]
Even after knowing you have to raise that matrix to the A-1 power, it takes a lot of googling to get the matrix multiplication correct.