Two square matrices $A , B$ satisfy
$$A B + A ^ { 2 } B = E , \quad ( A - E ) ^ { 2 } + B ^ { 2 } = O$$
Which of the following statements in the given options are correct? (Here, $E$ is the identity matrix and $O$ is the zero matrix.) [4 points]
\textbf{Options}
$\text{ᄀ}$. The inverse matrix of $B$ exists.\\
$\text{ㄴ}$. $A B = B A$\\
$\text{ㄷ}$. $\left( A ^ { 3 } - A \right) ^ { 2 } + E = O$\\
(1) ㄴ\\
(2) ㄷ\\
(3) ᄀ, ㄴ\\
(4) ᄀ, ㄷ\\
(5) ᄀ, ㄴ, ㄷ