# Inverse matrix order of operation

If I have a rotation, $A$, and a translation, $B$, which I multiply like so

$C = AB$

Does the inverse of $C$ not only inverse the magnitudes of $A$ and $B$ but also become the reverse of operations?

e.g. $C^{-1} = BA$?

Does the inverse of a matrix also inverse the order of original operations (or am I conflating inverse with reverse)?

Yes. If you're compounding operations to make a matrix, then the inverse matrix will be the compound of the inverse operations, in the reverse order. So if $C = AB$ then $C^{-1} = B^{-1}A^{-1}$