Exercise 1.5.5 Let Y = (y1, y2)

 have a N(0, I ) distribution. Show that if A =



1 a a 1

B =



1 b b 1

, then the conditions of Theorem 1.3.7 implying independence of Y AY and Y BY are satisfied only if |a| = 1/|b| and a = −b.What are the possible choices for a and b?