Answer
a. $AB$=$\left[\begin{array}{lll}
-1 & -2 & -3\\
-2 & -4 & -6\\
-3 & -6 & -9
\end{array}\right]$
b. $BA=[-14]$
Work Step by Step
The product of an $m\times\underline{n}$ matrix $A$ and an $\underline{n}\times p$ matrix $B$
is an $m\times p$ matrix $AB$.
The element in the ith row and $j\mathrm{t}\mathrm{h}$ column of $AB$ is found by
multiplying each element in the ith row of $A$ by the corresponding element in the $j\mathrm{t}\mathrm{h}$ column of $B$
and adding the products.
-----------------
a.
$A$ is a $3\times\underline{1}$ matrix, B is a $\underline{1}\times 3$ matrix
$AB$ exists, and is a $3\times 3$ matrix.
$AB=\left[\begin{array}{lll}
-1(1) & -1(2) & -1(3)\\
-2(1) & -2(2) & -2(3)\\
-3(1) & -3(2) & -3(1)
\end{array}\right]$=$\left[\begin{array}{lll}
-1 & -2 & -3\\
-2 & -4 & -6\\
-3 & -6 & -9
\end{array}\right]$
b.
$B$ is a $1\times\underline{3}$ matrix, $A$ is a $\underline{3}\times 1$ matrix
$BA$ exists, and is a $1\times 1$ matrix (single number).
$BA=[1(-1)+2(-2)+3(-3)]=[-1-4-9]$
$BA=[-14]$
