Question

If a matrix has $24$ elements, what are the possible orders it can have? What, if it has $13$ elements?

Answer 1

Since matrix has $24$ elements,
$\text{No. of rows}\times \text{No. of columns}=24$
$1\times 24=246\times 4=24$
$2\times 12=248\times 3=24$
$3\times 8=2412\times 2=24$
$4\times 6=2424\times 1=24$
Hence, possible orders are
$1\times 24,2\times 12,3\times 8,4\times 6,6\times 4,8\times 3,12\times 2,24\times 1$

If matrix has $13$ elements.
$\text{No. of rows}\times \text{No. of columns}=13$
$1\times 13=13$ or $13\times 1=13$
Hence, possible orders are $1\times 13$ and $13\times 1$.