If $A$ and $B$ are two matrices and $(A + B)(A - B) = A^2 - B^2$,then

If $A = \begin{bmatrix} 5 & -3 \\ 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 6 & -4 \\ 3 & 6 \end{bmatrix}$,then $A - B = $

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & 3 & -1 \\ 3 & 1 & 2 \end{bmatrix}$ and $I$ is a unit matrix of $3^{rd}$ order,then $(A^2 + 9I)$ equals

Let $A$ and $B$ be any two $3 \times 3$ symmetric and skew-symmetric matrices respectively. Then which of the following is $NOT$ true?

$A$ manufacturer produces three products $x, y, z$ which he sells in two markets. Annual sales are indicated below:

Market	$x$	$y$	$z$
$I$	$10,000$	$2,000$	$18,000$
$II$	$6,000$	$20,000$	$8,000$

If the unit sale prices of the above three commodities are $Rs. 2.50, Rs. 1.50$ and $Rs. 1.00$ respectively,and unit costs are $Rs. 2.00, Rs. 1.00$ and $50$ paise respectively,find the total gross profit.

If for $A = \begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$,$A^2 = I$,then . . . . . . .