Computing Fibonacci Numbers

After some clever rewriting, we can square $M^n$ in only three squares, as shown below. We simply compute $(a + b)^2, a^2$ , and $b^2$ and then add and multiply them together in various combinations to get the new values of the matrix.

After some clever rewriting, we can square $M^n$ in only three squares, as shown below. We simply compute $(a + b)^2, a^2$ , and $b^2$ and then add and multiply them together in various combinations to get the new values of the matrix.