Suppose That $A$ Is A $1 \times n$ Matrix And $B$ Is A $n \times 1$

Essay

Suppose that $A$ is a $1 \times n$ matrix and $B$ is a $n \times 1$ matrix.
(a) Can $A B$ be found? If so, give the dimensions of the resulting matrix.
(b) Can $B A$ be found? If so, give the dimensions of the resulting matrix.
(c) Does $A B=B A$ ? Explain why or why not.
(d) If $C$ and $D$ are each square matrices, will $C D$ always exist?