Where does the identity matrix comes from in $(\alpha I - A) \vec X = 0$

Question

Let $\alpha$ be a number, $A$ a matrix, then

$\alpha \vec X = A \vec X$

becomes

$(\alpha I - A) \vec X = 0$

Where does the $I$ come from?

Answer 1

It's a trick. Since $X = IX$, then $aX = a(IX) = (aI)X$.