I am asked to prove; $$(AB)^T=B^TA^T$$ although it is very simple to prove it by the straight forward way, in the exercise I am asked to prove it without using subscripts and sums, directly from the following property of inner product of real vectors:$$\langle A\textbf{x},\textbf{y}\rangle =\langle \textbf{x},A^T\textbf{y}\rangle$$

Where $A$ is an $m\times n$ real matrix, $x \in \mathbb{R}^n$,$y \in \mathbb{R}^m$ 

I don't know how to approach this problem, any suggestions?