Symmetric bilinear form/Nondegenerate/Sign of determinant and sign change/Exercise

Let ${}\left\langle -,-\right\rangle$ be a nondegenerate symmetric bilinear form of type ${}(n-q,q)$ on an ${}n$-dimensional real vector space. Let ${}v_{1},\ldots ,v_{n}$ be a basis of ${}V$, and let ${}G$ denote the Gram matrix of ${}\left\langle -,-\right\rangle$ with respect to this basis. Show that the sign of ${}\det G$ equals ${}(-1)^{q}$.

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