If $A=\left(\begin{array}{ll}1& 2\\ 2& 3\end{array}\right)$ and $A^2-kA-I_2=O,$ where $I_2$ is the $2\times 2$ identity matrix. Then what is the value of $k$?

Consider the following in respect of matrices $A$ and $B$ of same order
$1$. $A^2-B^2=(A+B)(A-B)$
$2$. $(A-I)(I+A)=O\iff A^2=I$
where $I$ is the identity matrix and $O$ is the null matrix.

Which of the above is/are correct?