The number of matrices of order $3 \times 3$,whose entries are either $0$ or $1$ and the sum of all the entries is a prime number,is:

Two farmers,Ramkishan and Gurcharan Singh,cultivate only three varieties of rice: Basmati,Permal,and Naura. The sales (in Rupees) of these varieties of rice by both farmers in the months of September and October are given by the following matrices $A$ and $B$.
September Sales (in Rupees)
$A = \begin{bmatrix} \text{Basmati} & \text{Permal} & \text{Naura} \\ 10,000 & 20,000 & 30,000 \\ 50,000 & 30,000 & 10,000 \end{bmatrix} \begin{matrix} \\ \text{Ramkishan} \\ \text{Gurcharan Singh} \end{matrix}$
October Sales (in Rupees)
$B = \begin{bmatrix} \text{Basmati} & \text{Permal} & \text{Naura} \\ 5,000 & 10,000 & 6,000 \\ 20,000 & 10,000 & 10,000 \end{bmatrix} \begin{matrix} \\ \text{Ramkishan} \\ \text{Gurcharan Singh} \end{matrix}$
$(i)$ Find the combined sales in September and October for each farmer in each variety.
$(ii)$ Find the decrease in sales from September to October.
$(iii)$ If both farmers receive $2\%$ profit on gross sales,compute the profit for each farmer and for each variety sold in October.

The order of $[x\,y\,z]\,\,\left[ {\begin{array}{*{20}{c}}a&h&g\\h&b&f\\g&f&c\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right]$ is

In the matrix $A = \begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt{3} & 1 & -5 & 17 \end{bmatrix}$,write:
$(i)$ The order of the matrix
$(ii)$ The number of elements
$(iii)$ The elements $a_{13}, a_{21}, a_{33}, a_{24}, a_{23}$

If $A = \begin{bmatrix} 0 & 3 \\ 0 & 0 \end{bmatrix}$ and $f(x) = x + x^2 + x^3 + \ldots + x^{2023}$, then $f(A) + I = $

Let $A = \begin{bmatrix} -3 & 2 \\ 1 & 4 \end{bmatrix}$. If $A^2 - 2A + I = \begin{bmatrix} 18 & p \\ q & 11 \end{bmatrix}$, find the values of $p$ and $q$.