Compute the Jacobian ${\partial (x,y)}/{\partial (u,v)}$ after solving for x and y in terms of u and v.
u=x+y and v=x-y
I have solved for x and y as follows:
$x=(u+v)/2$
$y=(u-v)/2$
I have calculated the determinant of the Jacobian matrix to be
det($\begin{bmatrix}y & x\\ -y & x\end{bmatrix}$)=$1/2*(u^2-v^2)$
The determinant is meant to be 1/2. How do I get from my determinant to -1/2?