Considering the bases and find the transitition matrix .

I know this is really simple, but I can never remember which way it is meant to go. Is the matrix that takes matrix to matrix ? 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,