Question

Good morning,

I have this question:

the matrix
A = 0 6
4 12

i) show that it is invertable.

ii)Find the equation of the image f(c) of the unit circle c in the form.
ax^2+bxy+cy^2=d

iii)Calculate the area enclosed by f(c).
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So far I have found the determinant which is -24 and the inverse matrix which is

A = -1/2 1/4
1/6 0

So the xy coords are
(-1/2x+1/4y,1/6x+y)

Which lead me to the following equation 5x^2/18+xy/12+17y^2/16=1

So now I need to calculate the area which I understand is essentially pie multiplied by the scalar quantity that is the determinant.

So -24pi. Since the det is negative I assume it has 'flipped' the transformation but what does this mean for the area?

I assume ive gone wrong somewhere.

Anyone have any pointers?
Thanks