Why if we rotate an object by R and then translate it with T, from the object perspective, we're actually applying $-T$ and then $-R$
If you have object$\rightarrow$world space transformation matrix:
$$M=T*R$$
then inverse (i.e. world$\rightarrow$object) of this transformation matrix is:
$$M^{-1}=(T*R)^{-1}=R^{-1}*T^{-1}$$
So the order of multiplication of matrix inverses is reversed per matrix inversion rules.