If B≈A with (P^-1)*A*P = B and also (Q^-1)*A*Q = B, show that Q=RP where R is a nonsingular matrix that commutes with A.
AR = RA
The Attempt at a Solution
Our professor told us that it is easier to just play around with these equations and get the answer. That breaking them down to their elements would be a ton of work. I tried multiplying by a bunch of various ways. First I changed the equivalence formulas to, AP=PB and AQ=QB, and I tried multiplying by R, because of the commuting factor, but I couldn't get anywhere doing that. If someone could give me a hint as to if I'm missing a property or something that could help me out, that'd be great. Thanks.