$A = \begin{bmatrix} a & b\\ c& d \end{bmatrix}$
$\left | A \right | = ad - cb$
For max $cb$ must be $0$
$\left | A \right | = ad$
$a + d = -6$
$a$ and $d$ cannot be +tive as the sum will not be -6
if $a$ is +tive or $d$ is -tive or vice versa then it will not give the maximum value [ product will be not maximum]
Possible values of $a$ and $d$
$a$ |
$d$ |
$a+d$ / $a.d$ |
$0$ |
$-6$ |
$-6 / 0$ |
$-1$ |
$-5$ |
$-6 / 5$ |
$-2$ |
$-4$ |
$-6 / 8$ |
$-3 $ |
$-3$ |
$-6 / 9$ $\bigstar$ |