Exercise 4.2.32

Since $P_{1}b$ is in $C(A)$ and $P_2$ projects onto that column space, $P_2\left(P_{1}b\right)$ equals $P_{1}b$. So $P_2{P}_1=P_1=a{a}^T∕a^{T}a$ where $a=(1,2,0)$.