Symmetric bilinear form/Nondegenerate/Gram determinant/Exercise

Let ${\displaystyle {}V}$ be an ${\displaystyle {}n}$-dimensional real vector space, and let ${\displaystyle {}\left\langle -,-\right\rangle }$ denote a symmetric bilinear form on ${\displaystyle {}V}$. Show that the following properties are equivalent.

1. The bilinear form is nondegenerate.
2. The Gram matrix of the bilinear form with respect to any basis is invertible.
3. The bilinear form is of type ${\displaystyle {}(p,n-p)}$ (with some ${\displaystyle {}p\in \{1,\ldots ,n\}}$).