With $(AB^{-1})^T$, what comes first, the multiplication or the transpose? In part of the question we have $(AB^{-1})^T$.
My first thought was that I multiply $A$ and $B^{-1}$, then apply the transpose.
But according to theory $(AB)^T = (B)^T(A)^T,$ so this says I should get the transpose first, then multiply.
I'm confused about either sticking to the theory or what I did was right.

The order is unimportant from a principles standpoint, but in some situations one formula may be more useful than the other. The identity $(AB)^T=B^TA^T$ is an algebraic tool to prove theorems and solve equations, it isn’t necessarily a computational tool. $(B^{-1})^TA^T=(AB^{-1})^T$, calculate whichever feels more natural (I’d go for the RHS myself).
