The variable $(X,Y)$ is uniformly distributed over $$D=\{(x,y)\in\mathbb R^2:|x|+|y|\le1\}.$$ Let $$A=X-Y,B=X+Y.$$ Are $A$ and $B$ independent?
I tried to prove $F(AB)=F(A)F(B)$, I tried to find the joint function of $AB$ through changing variables. $X=(A-B)/2$ and $Y=(A+B)/2$ and got that the joint function is $F(AB)=C/2$. How do I continue from here? How can I find the marginal functions to check if the equation is correct?