Answer
a. False.
b. False.
c. True.
d. True.
e. False.
Work Step by Step
a. $AB=\begin{bmatrix}A\vec{b}_{1}&A\vec{b}_{2}\end{bmatrix}$. The matrix products $\vec{a}_{1}\vec{b}_{1}$ and $\vec{a}_{2}\vec{b}_{2}$ are not even defined for $2\times 1$ column vectors.
b. Each column of $AB$ is a linear combination of the columns of $A$ with weights from the corresponding column of $B$. The description given inverts the roles of $A$ and $B$. (See the beige box on page 97.)
c. This is the result of Theorem 2(b) on page 99.
d. This is the result of Theorem 3(b) on page 101.
e. The order is not the same, but reversed, as indicated by Theorem 3(d).
