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

$(1 \times 13), (13 \times 1)$

The correct answer is Option (2) → $(1 \times 13), (13 \times 1)$ ##

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

We have, $m \times n = 28$

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

So, 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 $1 \times 13, 13 \times 1$.