This is related to a previous question I asked. But I realize that my logic there is total bonkers. And it would be great if someone could help me out a bit.
$B:V\times V\to F$ is a bilinear form where $V$ is a finite-dimensional vector space.
$X\leq V$ is a subspace which is also the annihilator of another subspace $Y\leq V$ wrt $B$.
I am given that $B|_X$ is nonsingular.
I wish to show that it follows that $B$ itself is nondegenerate.