If A is an x matrix and X is an x1 column matrix and U is a subspace such that

Show that since A is an orthogonal matrix:

<< for those who don't know the notation. simply means the corresponding eigenvector of with respect to the eigenvalue, 1.

Someone wanna give me a hand? Here's what I did. I stated that since A is orthogonal, we know that

then i went ahead and did

multiplying both sides by A

<<< since since A is orthogonal

and now i'm stuck.. don't know where to go next..

Any help appreciated! =D