Let $A$ be a $2 \times 2$ real matrix and $I$ be the identity matrix of order $2$. If the roots of the equation $|A-xI|=0$ are $-1$ and $3$,then the sum of the diagonal elements of the matrix $A^2$ is $..............$

If $A$ and $B$ are $3 \times 3$ matrices and $|A| \neq 0$,then which of the following are true?

Let $m$ and $M$ be respectively the minimum and maximum values of $\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$. Then the ordered pair $(m, M)$ is equal to

If $A = \begin{bmatrix} 3 & 4 \\ 5 & 6 \end{bmatrix}$ and $B = \begin{bmatrix} x & 0 \\ 0 & y \end{bmatrix}$,where $x, y \in \mathbb{N}$,then:

If matrix $A = [a_{ij}]_{3 \times 3}$ and $B = [b_{ij}]_{3 \times 3}$,where $a_{ij} + a_{ji} = 0$ and $b_{ij} - b_{ji} = 0$ for all $i, j$,then $A^4B^3$ is:

Let $A = \begin{bmatrix} 1 & 2 \\ 1 & \alpha \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 3 \\ \beta & 2 \end{bmatrix}$. If $A^2 - 4A + I = O$ and $B^2 - 5B - 6I = O$, then among the two statements:
(S1): $[(B - A)(B + A)]^T = \begin{bmatrix} 13 & 15 \\ 7 & 10 \end{bmatrix}$
and
(S2): $\det(\text{adj}(A + B)) = -5$.