mpower / matrix power multiplication

How does MATLAB calculate the power of a matrix, especially for large numbers?

I'm doing some markov chain work where I need to multiply a large (nxn) matrix by a large positive integer. I couldn't find in their documentation how it does it. Based on the speed at which it is performing I find it hard to believe it is simply consecutive squaring.

[Stephen23]

This Wikipedia article shows that there are quite few algorithms faster than a naïve repeated multiplication:

https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm

You would have to ask TMW which algorithm/s they use.