If $P = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}$, then $P^5$ is equal to

If $A = \begin{bmatrix} ab & b^2 \\ -a^2 & -ab \end{bmatrix}$ and $A^n = O$,then the minimum value of $n$ is

Which of the following statements is not correct?

Let $A = [a_{ij}]$ be a real matrix of order $3 \times 3$,such that $a_{i1} + a_{i2} + a_{i3} = 1$,for $i = 1, 2, 3$. Then,the sum of all the entries of the matrix $A^3$ is equal to:

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

Factory	Men and Women Workers
$I$	$30$ Men,$25$ Women
$II$	$25$ Men,$31$ Women
$III$	$27$ Men,$26$ Women

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?

What are the values of $(x, y, z, t)$,if $3\begin{bmatrix} x & y \\ z & t \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2t \end{bmatrix} + \begin{bmatrix} 4 & x+y \\ z+t & 3 \end{bmatrix}$?