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

Find the order of the matrix product $\mathrm{AB}$ and the product $\mathrm{BA}$ , whenever the products exist.
- $\mathrm{A}$ is $4 \times 1, \mathrm{~B}$ is $1 \times 4$ .

A) $\mathrm{AB}$ is $4 \times 4, \mathrm{BA}$ is $1 \times 1$ .
B) $\mathrm{AB}$ is $4 \times 4$ , $\mathrm{BA}$ is nonexistent.
C) $\mathrm{AB}$ is nonexistent, $\mathrm{BA}$ is $1 \mathrm{x} 1$ .
D) $\mathrm{AB}$ is $1 \times 1$ , BA is $4 \times 4$ .