Question

How many matrices of different orders can be obtained with $36$ elements?

Answer 1

Total elements in matrix$=36$

$\therefore$ Possible matrices are

$6\times 6$ ($6$ rows $6$ columns)

$1\times 36$ ($1$ row $36$ columns)

$36\times 1$ ($36$ rows $1$ columns)

$18\times 2$ ($18$ rows $2$ columns)

$2\times 18$ ($2$ rows $18$ columns)

$9\times 4$ ($9$ rows $4$ columns)

$4\times 9$ ($4$ rows $9$ columns)

$12\times 3$ ($12$ rows $3$ columns)

$3\times 12$ ($36$ rows $12$ columns)

$\therefore$ Total matrices $=9$

Answer$=9$