Transpose of 2 matrices together

Question

So if I have an $m\times n$ matrix $A$ and I represent that matrix as $\displaystyle A = QR$, how do I write $A^{T}$ (transpose) in terms of the original $\displaystyle QR$? Does it become $\displaystyle Q^{T}R^T$ or $\displaystyle R^{T}Q^{T}$? or something else? What about for the inverse?

Answer 1

$(AB)^T=B^TA^T$.

That's because

$$A^T_{ij}=A_{ji}=\sum_{k=1}^{m}Q_{jk}R_{ki}=\sum_{k=1}^m R_{ik}^TQ_{kj}^T=(R^TQ^T)_{ij}$$