Matrix inverse and Change of basis

Question

I have 2 Change of Basis Matrices $ S_{A,B} $ and $ S_{A,C}$

I want determinate $ S_{C,B} $

We know that

$$ S_{A,B} S_{B,C} = S_{A,C} $$ $$ S_{B,C} = S_{A,B}^{-1} S_{A,C} $$

Now i'm quite not sure if $$ S_{C,B} = S_{B,C}^{-1} = S_{A,B} * S_{A,C}^{-1} \space\space (1) $$

or

$$ S_{C,B} = S_{B,C}^{-1} = S_{A,C}^{-1} *S_{A,B} \space\space (2) $$

if it's (2) why ?

Answer 1

In general, if $A$ and $B$ are invertible, then $(AB)^{-1} = B^{-1}A^{-1}$. So which of (1) and (2) fits that pattern?