P and A are 2x2 matrices.

Is the following true?

P^{-1}AP = APP^{-1}

Do they both simply simplify to A?

I had a few examples (using real matrices) that this is true. Though I'm not entirely sure since it could be some kind of luck. Interestingly I can never get:

PAP^{-1}=AP^{-1}P

Guest Jul 21, 2017