graphics - Transformations between coordinate systems

In a graphics engine, I have three three-dimensional orthogonal coordinate systems, O, A and B.

A and B are the result of two different transformations from O. I now want to calculate the transformation matrix R, which takes you from A to B. R should be the rotation and translation with respect to coordinate system A, not the original coordinate system O.

Which of the following is correct?

(1) B = A * R or (2) B = R * A

By doing some simple worked examples, it seems that (1) is correct. However, my intuition says that (2) is correct, because the transformation to A should be applied before the transformation to B, via R. Which is it?

Thanks :)