Symmetric bilinear form/K/Eigenspace/0/Degeneracy space/Exercise

Let ${}V$ be an finite-dimensional ${}K$-vector space, endowed with a symmetric bilinear form ${}\left\langle -,-\right\rangle$. Let ${}M$ be the Gram matrix of the form with respect to a given basis of ${}V$. Show that the eigenspace to the eigenvalue ${}0$ of ${}M$, considered as a linear mapping of ${}V$ to ${}V$ with respect to this basis, equals the degeneracy space of the form.

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