Help needed with martices and conics

I'm not sure this is where I should put this, but I didn't see anywhere else:

1)

Using the determinant of a matrix representing a conic,

[a b d]

[b c e]

[d e f]

where the equation of the conic is

ax^2=2bxy+cy^2+2dx+2ey+f=0

and the determinant of the top left 2-by-2 matrix, how would you classify the conic?

2) (Refering to the d and e of the previous question)

Show that d^2+e^2 stays the same under a rotation of axes, in other words, the matrix is multiplied by

[cos(z) -sin(z) 0]

[sin(z) cos(z) 0]

[0 0 1]

Note: It's a 3x3 matrix

Thanks in advance!