This is a homework problem i had. Help!

Explain why the dot product ofxand y equals the dot product ofPxandPy.

Then From (Px)^T(Py)=x^Ty deduce thatP^TP=I for any permutation. Withx=(1,2,3) andy=(1,4,20) choosePto show thatPxdotyis not alwaysxdotPy.