Answer
a. columns, rows
b. BA and AA are defined.
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 $B.$
---
a.
Fill the blanks with:
... {\bf columns} ...in the first matrix ... {\bf rows} ...in the second matrix
.
b.
$AB$ is 3$\times\color{blue}{3}$ multiplied with a $\color{blue}{4}\times$3 ... not possible.
$BA$ is $4\times\color{blue}{3}$ multiplied with a $\color{blue}{3}\times$3 ... possible
$AA$ is $3\times\color{blue}{3}$ multiplied with a $\color{blue}{3}\times$3 ... possible
$BA$ is $4\times\color{blue}{3}$ multiplied with a $\color{blue}{4}\times$3 ... not possible.
BA and AA are defined