Two $2 \times 2$ square matrices $A, B$ satisfy
$$2A^2 + AB = E, \quad AB + BA = 2A + E$$
Which of the following statements are correct? Choose all that apply from $\langle$Remarks$\rangle$. (Here, $E$ is the identity matrix.) [4 points]
\textbf{Remarks}\\
ᄀ. $A^{-1} = 2A + B$\\
ㄴ. $B = 2A + 2E$\\
ㄷ. $(B - E)^2 = O$ (Here, $O$ is the zero matrix.)\\
(1) ㄴ\\
(2) ㄷ\\
(3) ᄀ, ㄴ\\
(4) ᄀ, ㄷ\\
(5) ᄀ, ㄴ, ㄷ