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Proof with Transformations and Subspaces

I have this proof that I cannot figure out. If anyone could give me a little headstart that would be great. I am still struggling to fully grasp the concepts so maximum explanation is useful please.

Also I dont know how to make the perp symbol that looks like an upside down T so ill use an L instead.

V^L=V perp

W __c__ V means W is a subspace of V

Suppose that A is a real symmetric n x n matrix. Show that if V is

a subspace of Rn and that A(V) __c__ V, then A(V^L) __c__ V^L.

Attachment 19900

Any help??!?!

Thanks