Let $S\subset M_{n}(\mathbb{R})$ be the singular points of the equation $Det=0$. That is $S$ is the critical points of the determinant function.
>What  matrices belongs to $S$, precisely?

Let $M=Det^{-1}\{0\}-S$ be the codimension one submanifold of $M_{n}(\mathbb{R})$  which has  a natural Riemannian metric induced by the standard metric of $M_{n}(\mathbb{R})\simeq\mathbb{R}^{n^{2}}.$

>What is  a linear  algebraic  and matrix meaning for  a  matrix $A\in M$ with the  following  property:

**"The sectional curvature of $M$ at $A$ is  independent of  choosing a $2$-plane tangent to $M$ at $A$"**

>What  is  a precise example of this  situation, for $n=2$?