This is LaTeX code:

[latex]
 
\displaystyle
$\begin{align}
x \in Ker(A + I) \ & \Leftrightarrow \ (A + I) x = 0 \ \Leftrightarrow \ A x + I x = 0 \ \Leftrightarrow \ A x + x = 0 \ \Leftrightarrow \ A x - x = - 2 x \\
& \Leftrightarrow \ A x - I x = - 2 x \ \Leftrightarrow \ (A - I) x = - 2 x \ \Leftrightarrow \ (A - I)\left( -\frac{1}{2} x \right) = x \ \Leftrightarrow \ x \in Im(A - I)
\end{align}$
 
[/latex]