Fibonacci matrix-exponentiation

Fibonacci matrix-exponentiation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Fibonacci sequence defined with matrix-exponentiation:

      F0 = 0 
      F1 = 1 

${\begin{pmatrix}F_{n+1}\\F_{n}\end{pmatrix}}={\begin{pmatrix}1&1\\1&0\end{pmatrix}}^{n}{\begin{pmatrix}F_{1}\\F_{0}\end{pmatrix}}$

Task

Write a function using matrix-exponentiation to generate Fibonacci number for n = 2³² and n = 2⁶⁴.

Display only the 20 first digits and 20 last digits of each Fibonacci number.

Extra

Generate the same Fibonacci numbers using Binet's formula below or another method.

$F_{n}={\cfrac {\varphi ^{n}-(-\varphi )^{-n}}{\sqrt {5}}}$

$\varphi ={\cfrac {1+{\sqrt {5}}}{2}}$

Related tasks

•   Fibonacci sequence
•   Matrix-exponentiation operator