Simple composition of linear maps

Question

Let $F : R^2 → R^2$ s.t. $x → (−x_2, x_1)$ and $G: R^2 → R^2$ s.t $x → (x_2, sin x_1)$. Evaluate $G ◦ F$ and $F ◦ G$.

I have said $(G ◦ F)(x) = G(F(x))=-x_2,sinx_1$, but I feel as though this is wrong, can someone give me a pointer?

Answer 1

It is

$$(F\circ G)(x_1,x_2)=F(x_2,\sin x_1)=(-\sin x_1,x_2)$$ and

$$(G\circ F)(x_1,x_2)=G(-x_2,x_1)=(x_1,-\sin x_2).$$