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.
- $\mathrm{A}$ is $2 \times 1, \mathrm{~B}$ is $1 \times 1$ .

A) $\mathrm{AB}$ is $2 \times 1, \mathrm{BA}$ is nonexistent.
B) $\mathrm{AB}$ is nonexistent, $\mathrm{BA}$ is $1 \times 2$ .
C) $\mathrm{AB}$ is $1 \times 2, \mathrm{BA}$ is $1 \times 1$ .
D) $\mathrm{AB}$ is $2 \times 2, \mathrm{BA}$ is $1 \times 1$ .