Matrices & Systems · Challenge problem

Invertible $2\times 2$ matrices $A$ and $B$ have $A^{-1} = \begin{pmatrix}1 & 2\\0 & 1\end{pmatrix}$ and $B^{-1} = \begin{pmatrix}3 & 0\\1 & 1\end{pmatrix}$. Find the entry in row 2, column 1 of $\big((AB)^{T}\big)^{-1}$.