Find a 3x3 matrix A such that \( \mathbf A\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} g & h & i \\ a & b & c \\ d & e & f \end{pmatrix}.\)

I don't really know where to start because I can't wrap my head around the fact that the letters switch. Help, please!

Also, don't solve the problem for me because I want to figure it out myself. Just a few hints please :)

MobiusLoops May 19, 2022