Find the Order of the Matrix Product $\mathrm{AB}$ And the Product $\mathrm{BA}$

Multiple Choice

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist.
- $A$ is $1 \times 3$ , B is $1 \times 3$ .

A) $\mathrm{AB}$ is $3 \times 1$ , BA is $1 \times 3$ .
B) $\mathrm{AB}$ is $1 \times 1, \mathrm{BA}$ is $3 \times 3$ .
C) $\mathrm{AB}$ is $1 \times 3, \mathrm{BA}$ is $3 \times 1$ .
D) $\mathrm{AB}$ is nonexistent, $\mathrm{BA}$ is nonexistent.