I am having trouble with this proof.
A matrix B is similar to A if there exists a nonsingular matrix P such that
PAP^-1=B
The question is:
Prove if B is similar to A then A is similar to B
I have:
Assume B is similar to A. Then there exists P such that
PAP^-1=B.
multiplying both sides by P gives
PA=BP
then multiplying both sides by inverse of P gives
A=P^-1 *B*P
but I need to show A=PBP^-1. and I cannot figure it out. Thanks!!!!!!!
Thanks Tonio! I actually skipped class the day the professor described invertible matricies (had to work on some homework that was due that day haha) but this solution sounds elegant and beautiful =D Thanks alot!!!!!!!!!!!!
EDIT: aah now I see invertible just means AB=BA=I