very simple, change of basis.

Considering the bases $\displaystyle S = (1,0),(0,1) $ and $\displaystyle B = (2,1),(3,2)$ find the transitition matrix $\displaystyle P_{S,B} $.

I know this is really simple, but I can never remember which way it is meant to go. Is $\displaystyle P_{S,B} $ the matrix that takes matrix $\displaystyle B $ to matrix $\displaystyle S $? or the other way around?

Seeing as S can be written as an identity matrix, the transition matrix taking S to B is just going to be B right?

Then to find the transition matrix to take B to S, I can jus take the inverse?

Thanks in advance,