Q:

Matrix 2x2 named A

$A^2 + A - 6I = 0$
A= $\begin{bmatrix}a & b\\c & d\end{bmatrix}$
I was asked to find
$a + d$, and $ad - bc$
$a+d>0$
What i get is 
$A^2$ = $\begin{bmatrix}a^2+bc & ab + bd\\ac+dc & bc+d^2\end{bmatrix}$
I get
$a^2+bc+a=6, $
$ab+bd+b = 0,$
$bc+d^2+d=6, $
$ac+dc+c=0$
I get a=-1/2, d=-1/2
Why i get wrong answer? Please help me?

A:

You have that
$$(A+3I)(A-2I)=0$$
so the matrix
$$A=2I=\pmatrix{2&0\\0&2}$$
is a valid such $A$.

