I cannot start the following exercise. Let $V$ be a complex vector space such that $\operatorname{dim}V=n$ and $B=(\underline{e}_1,\ldots,\underline e_n)$ a basis for $V$. Let also $g:V\times V\longrightarrow\mathbb{C}$ a sesquilinear map with associated matrix $G$ with respect to $B$ of the form $$ G=\overline{A}^TA $$ for an invertible matrix $A\in\mathbb{C}_{n\times n}$. Prove that $g$ is an Hermitian scalar product.
Some ideas?
Thank You