Exercise 4.4.34

(a) $Qu=\left(I-2u{u}^T\right)u=u-2u{u}^{T}u$. This is $-u$, provided that $u^{T}u$ equals 1

(b) $Qv=\left(I-2u{u}^T\right)v=u-2u{u}^{T}v=u$, provided that $u^{T}v=0$.