If A be any  $m\times n$ matrix and both AB and BA are defined prove that B should be  $m\times n$ matrix 

In the matrix, write :
$A=\left[\begin{array}{c}2\\ 35\\ \sqrt{3}\end{array}\begin{array}{c}5\\ -2\\ 1\end{array}\begin{array}{c}19\\ \frac{5}{2}\\ -5\end{array}\begin{array}{c}-7\\ 12\\ 17\end{array}\right]$

(i) The order of the matrix
(ii) The number of elements 
(iii) Write the elements $a_{13},a_{21},a_{33},a_{24},a_{23}$

The possibility for the formation of rectangular matrices in the matrix algebra are