I was reading this post about bilinear maps and it raised some questions in my mind, for which I am not so sure about the answers.
It is proven there that for any symmetric bilinear form, it is degenerated if and only if the associated matrix is invertible.
1) So is it possible, if the form is not symmetric and non-degenerated to have a non-invertible matrix?
2) Is it possible to have a non-symmetric form which is degenerated such that the matrix is still invertible?
3) Also, is it possible to have a non-degenerated form that is "degenerated in the first variable", i.e. $q(x,y)=0 \forall y \rightarrow x=0$ but $\exists y \neq 0$ such that $q(x,y)=0 \forall x$?
