If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

As we know,, if a matrix is of order $m \times n$, it has $mn$ elements, where $m$ and $n$ are natural numbers.

We have, $m \times n = 28$
$\Rightarrow$ $(m,n) = \{ (1,28),(2,14),(4,7),(7,4),(14,2),(28,1)\}$

Therefore, the possible orders are $1 \times 28,2 \times 14,4 \times 7,7 \times 4,14 \times 2,28 \times 1$.

Also, if it has 13 elements, then $m \times n = 13$
$\Rightarrow$ $(m,n) = \{ (1,13),(13,1)\}$

Hence, the possible orders are $1 \times 13,13 \times 1$.