The question is:
Show that the following defines an inner product on $\mathbb{R}^2$: $$ \langle ( x_1 , y_1 ) , ( x_2 , y_2) \rangle = x_1 y_1 + 2 x_1 y_2 + 2 x_2 y_1 + 8 x_2 y_2 $$
Tried to show that $\langle ( x_2 , y_2) , ( x_1 , y_1) \rangle$ is the same thing but came at a roadblock (it isn't).
It's a past exam, and the solution says that the inner product is defined by $X_1^T A X_2$ where $$ A = \begin{pmatrix} 1&2\\2&8 \end{pmatrix} $$
The exam is in two days, so any help would be greatly appreciated.