If  $a_{ij}$  is the element of  $i^{th}row{j}^{th}$ column of a  $3\times 3$ matrix A &
(i) If  $(i<j)$  then  $a_{ij}$  is number of ways of distributing $(j+1)$  identical objects to $(i+1)$ person so that each one may receives none, one or more.
(ii) If  $(i>j)$  then $a_{ij}$  is number of ways of distributing $(i+1)$  distinct objects to $(j+1)$  person so that each one may receive any number of objects
(iii) If  $i=jthen{a}_{ij}=\max [i^{j+1},{(i+1)}^j]then$