Consider the following information regarding the number of men and women workers in three factories $I,\,II$ and $III$

Represent the above information in the form of a $3 \times 2$ matrix. What does the entry in the third row and second column represent?

If $A = \left[ {\begin{array}{*{20}{c}}3&5\\2&0\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}1&{17}\\0&{ – 10}\end{array}} \right]$ then $|AB|$ is equal to

If $A = \left( {\begin{array}{*{20}{c}}i&1\\0&i\end{array}} \right)$, then ${A^4}$ equals

In a legislative assembly election, a political group hired a public relations firm to promote its candidate in three ways: telephone, house calls, and letters. The cost per contact (in paise) is given in matrix $A$ as

$A = \left[ {\begin{array}{*{20}{c}}
  {\mathrm {Cost\,\,per\,\,contact}} \\ 
  {40} \\ 
  {100} \\ 
  {50} 
\end{array}} \right]\begin{array}{*{20}{l}}
  {{\text{ Telephone }}} \\ 
  {{\text{ Housecall }}} \\ 
  {{\text{ Letter }}} 
\end{array}$

The number of contacts of each type made in two cities $\mathrm{X}$ and $\mathrm{Y}$ is given by

$B=$$\,\left[ {\begin{array}{*{20}{c}}
  {\mathrm {Telephone}}&{\mathrm {Housecall}}&{\mathrm {Letter}} \\ 
  {1000}&{500}&{5000} \\ 
  {3000}&{1000}&{10,000} 
\end{array}} \right]\,$ $\begin{array}{*{20}{c}}
  {} \\ 
  { \to X} \\ 
  { \to \,Y} 
\end{array}$.  Find the total amount spent by the group in the two cities $\mathrm{X}$ and $\mathrm{Y}$.