Question

For the matrices $A$ and $B$, the product $AB$ exists but $BA$ does not exist. What can you say about the order of $A$ and $B$?

Answer 1

Let order of $A$ be $m\times n$.
Order of $B$ be $n\times p$.
$A_{m\times n}$ $B_{n\times p}$ exists.
$B_{n\times p}$ $A_{m\times n}$ does not exists.

So $A$ and $B$ are not square matrices.