Hi, the array initialization and brackets changes are nice.
But about the matrix multiplication, that's a thing of taste, I think the first implementation is more readable and intuitive. Do you have any strong opinions why the matrix multiplication should be changed?

Hi, the array initialization and brackets changes are nice.
But about the matrix multiplication, that's a thing of taste, I think the first implementation is more readable and intuitive. Do you have any strong opinions why the matrix multiplication should be changed?

That's fair - it's mostly a literal optimization, as fetching a[0][0] multiple times creates a lot of overhead - grabbing the value once is faster.

For 100000 runs

OPT FIB: 0.527823s
UNOPT FIB: 0.579806s

I am aware that this is unlikely to be used in performance demanding situations, but I personally think it's a good idea to practice writing, and especially for beginners, show what optimal code looks like, if it doesn't significantly impact code usability.

You could also take the optimization one step further, and read the values of b once into temporary variables, which yields more significant differences:

OPT FIB: 0.440688s
UNOPT FIB: 0.584284s

I've decided to add a slightly more elegant solution which I think looks a bit nicer, and added an explanation as to how it works to be slightly educational about python's various features.

I also thought it would be nice to see how long each method takes, so I added some comparisons for the 25th Fibonacci number across all seven methods.

Great, this one is better, I'll merge it. But first, please restore the "testing" part, we need to follow the template.

The template doesn't specify anything for comparisons such as timing, so I'll let you decide how you want to handle that.

Thanks, I'll merge and delete the timing comparisons.
The point of the project is to compare only the Time Complexities (Python is used because it is simple and the most understandable language, so it should be easier for someone from another environment to implement the same solution).