I came across the problem which says:
The map $L\colon \mathbb R^{2}\rightarrow \mathbb R^{2}$ given by $L(x,y)= (x,-y)$ is
(a) differentiable everywhere in $\mathbb R^{2}$,
(b) differentiable only at $(0,0)$,
(c) $DL(0,0)=L$,
(d) $DL(x,y)=L$ for all $(x,y) \in \mathbb R^2$.
I do not know how to approach the problem.Any kind of hints will be helpful. Thanks everyone in advance for your time .