Answer
$a.\qquad[28 \ \ 21 \ \ 28]$
$ b.\qquad [28 \ \ 21 \ \ 28]$
Work Step by Step
If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix
(so the number of columns of $A$ is the same as the number of rows of $B$),
then the matrix product $AB$ is the $m\times k$ matrix
whose $ij$-entry is the inner product of the $i\mathrm{t}\mathrm{h}$ row of $A$ and the jth column of $B.$
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$a.$
$DA$ is defined ( a 1$\times$2 matrix multiplies a 2$\times$2 matrix)
$DA $ is a 1$\times$2 matrix.
$(DA)B$ is defined ( a 1$\times$2 matrix multiplies a 2$\times 3$ matrix)
$(DA)B$ is a 1$\times$3 matrix.
$DA=[7(2)+3(0) \ \ 7(-5)+3(7)]=[14 \ \ -14]$
$(DA)B=[14(3)+(-14)(1) \ \ 14(1/2)+(-14)(-1) \ \ 14(5)+(-14)(3)]$
$=[28 \ \ 21 \ \ 28]$
$b.$
$AB$ is defined ( a $ 2\times$2 matrix multiplies a 2$\times 3$ matrix)
$AB $ is a $2\times 3$ matrix.
$D(AB )$ is defined ( a $ 1\times$2 matrix multiplies a 2$\times 3$ matrix)
$D(AB )$ is a $ 1\times$3 matrix.
$AB=\left[\begin{array}{lll}
2(3)+(-5)(1) & 2(1/2)+(-5)(-1) & 2(5)+(-5)(3)\\
0(3)+7(1) & 0(1/2)+7(-1) & 0(5)+7(3)
\end{array}\right]=\left[\begin{array}{lll}
1 & 6 & -5\\
7 & -7 & 21 \\
& &
\end{array}\right]$
$D(AB )=[7(1)+3(7) \quad 7(6)+3(-7) \quad 7(-5)+3(21)]$
$=[28 \ \ 21 \ \ 28]$
