If a matrix has $18$ elements,what are the possible orders it can have? What,if it has $5$ elements?

(N/A) We know that if a matrix is of the order $m \times n$,it has $mn$ elements.
To find all possible orders of a matrix with $18$ elements,we need to find all ordered pairs of natural numbers $(m, n)$ such that $mn = 18$.
The factors of $18$ are $1, 2, 3, 6, 9, 18$.
The possible ordered pairs $(m, n)$ are $(1, 18), (18, 1), (2, 9), (9, 2), (3, 6), (6, 3)$.
Thus,the possible orders are $1 \times 18, 18 \times 1, 2 \times 9, 9 \times 2, 3 \times 6, 6 \times 3$.
Similarly,for a matrix with $5$ elements,we need to find all ordered pairs $(m, n)$ such that $mn = 5$.
Since $5$ is a prime number,its only factors are $1$ and $5$.
The possible ordered pairs are $(1, 5)$ and $(5, 1)$.
Thus,the possible orders are $1 \times 5$ and $5 \times 1$.