Calculate WTW$.$ What do you get? Why should we expect this result?

Enter the following vectors into MATLAB:Compute the norm of b and the norm of Wb$.$ What do you notice? Also compute the dot products $$a$,$ b$$ and $$Wa$,$ Wb$.$

One of the fundamental properties of orthogonal matrices is that they preserve norms of vectors and the standard inner product. $($You can define orthogonal matrices as the ones with this property, in fact.$)$