**Toolbox:**

- If a matrix is of order $m\times n$.It has mn elements.
- Thus to find all possible orders of a matrix with 18 elements.We will find all ordered pairs of natural numbers whose product is 8.

Thus all possible pairs of 18 are : $18=(1\times 18)(18\times 1)(2\times 9)(9\times 2)(6\times 3)(3\times 6)$

There are 6 matrices of order: $1\times 18,18\times 1,2\times 9,9\times 2,3\times 6,6\times 3$

If 5 elements: 5=$1\times 5$

There are two matrices with 5 elements: $1\times 5,5\times 1$.

Two matrices exists:

Column matrix $\rightarrow $A matrix is said to be a column matrix, if it has only one column.

$m\times 1=5\times 1$

Row matrix $\rightarrow$ A matrix is said to be a row matrix, if it has only one row.

$1\times n=1\times 5$