Let A, B, and C be nxn matrices,(adsbygoogle = window.adsbygoogle || []).push({});

I'm wondering

1. is it possible to simplify (ABC)^5 to expand it ( maybe into something like (A^5)(B^5)(C^5) )

2. what's the fastest way of solving (ABC)^5? I'm thinking actually multiply ABC out, then diagonalize it. Is there a faster way?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Raising a bunch of matrices to a power

**Physics Forums | Science Articles, Homework Help, Discussion**