Convert/create matrix

[luisfe]

Hi,

i have a 3x3 matrix which is A.

I want to accomplish the following:
BC = AB

B = a matrix
C = a diagonal matrix.

Im familiar with rules like
A + B = B + A (commutativity)
A + 0 = A
.. and so on.

But i can't get a start on my problem obove.
My only idea is to work with the inverse somehow..

 

[Dr.Peterson]

You are trying to diagonalize matrix A, since BC = AB is equivalent to BCB^-1 = A (if B is invertible).

Here is one source that explains the concept and the process: https://textbooks.math.gatech.edu/ila/diagonalization.html