Hi I'm new in Group's theory(I'm physicist) so i wanted to know if i was making it right with one proof exercise. (And I don't know how to type equations here lol)

(x,y) in R2 , we define A_1,A_2,A_3,A_4 as:

a)A_1(x,y)=(x,y)

b)A_2(x,y)=(-x,-y)

c)A_3(x,y)=(-x,y)

d)A_4(x,y)=(x,-y)

Show that this 4 operations under the operation of aplying one next to the other form a group. Show explicitly the inverse in every operation.

I'll shown what I understand:

with A_1 next to A_2

1) lock property

Let (x,y) be in R2

So, A_2(A_1(x,y))=(-x,-y) in R2

This is all i have. Please guide me, don't give me the answer. Because i really want understand this. Also I was thinking that maybe I misunderstood the exercise.