An inner product is defined as $(x,y)_E=[a_1\quad a_2 \quad\ldots \quad a_n]E^TE[b_1\quad b_2 \quad\cdots\quad b_n]^T$ where $x=a_1e_1+\cdots+a_ne_n$ and $y=b_1e_1+\cdots+b_ne_n$ are vectors with the $e_i$'s being the usual basis elements of $\mathbb{R}^n$.
Verify that this is an inner product.