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If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements.
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We know that if a matrix is of order $\mathrm{m} \times \mathrm{n}$, it has mn elements.
$$
\Rightarrow \quad 18=1 \times 18=2 \times 9=3 \times 6
$$
Thus, all possible ordered pairs of the matrix having 18 elements are:
$(1,18),(18,1),(2,9),(9,2),(3,6),(6,3)$
If it has 5 elements, then possible order are:
$(1,5),(5,1)$
$$
\Rightarrow \quad 18=1 \times 18=2 \times 9=3 \times 6
$$
Thus, all possible ordered pairs of the matrix having 18 elements are:
$(1,18),(18,1),(2,9),(9,2),(3,6),(6,3)$
If it has 5 elements, then possible order are:
$(1,5),(5,1)$
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