Linear Algebra Help: Struggling with Question 3 Part a)

[jtm]

I'm really really struggling on this question and am becoming very depressed from the stress that is being generated.

http://www.math.rutgers.edu/courses/250/250C-f05/f05lab6.pdf

Question 3 Part a) I've been stuck on it for hours. The last part where it talks about "show by algebraic calculation" Please help me. I'm really sad.

 

[jtm]

I've tried using dot products but I don't see how I can represent that into a matrix. I don't see how doing a dot product of a matrix with a transposed matrix is even possible. Q dot product Q' is the identity matrix somehow.. wouldn't it be all 0s since the vectors are all orthogonal to each other?