Being morse function for a determinant map on M(n)

Question

Show that the determinant map on M(n) is Morse function if n=2.

I know that f to be a morse function, all critical points for f must be nondegenerate.

But i dont know how i calculate the derivative of a determinant map

Answer 1

Well, you do have $n=2$, after all. So write the matrix as $\begin{bmatrix} x&y\\z&w\end{bmatrix}$, and then you have no problem differentiating the determinant function. :)