Let $A=\left[\begin{array}{ll}1 & 2 \\ 1 & \alpha\end{array}\right]$ and $B=\left[\begin{array}{ll}3 & 3 \\ \beta & 2\end{array}\right]$. If $A^2-4 A+I=O$ and $B^2-5 B-6 I=O$, then among the two statements :
(S1):

$$
[(\mathrm{B}-\mathrm{A})(\mathrm{B}+\mathrm{A})]^{\mathrm{T}}=\left[\begin{array}{cc}
13 & 15 \\
7 & 10
\end{array}\right]
$$

and
(S2): $\operatorname{det}(\operatorname{adj}(\mathrm{A}+\mathrm{B}))=-5$.