Let $A=\begin{bmatrix}1 & \sin\theta & 1\\-\sin\theta & 1 & \sin\theta\\-1 & -\sin\theta & 1\end{bmatrix}$, where $\theta\in[0,2\pi]$ then which of the following statements are correct?

A. $|A|=2+2\sin^2\theta$

B. Maximum value of $|A|$ is 1.

C. Maximum value of $|A|$ is –1.

D. $|A|\in[2,4]$

Choose the correct answer from the options given below:

If $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \begin{bmatrix} 3 & 5 \\ -1 & 3 \end{bmatrix} = \begin{bmatrix} m & 14 \\ 2 & n \end{bmatrix}$, then $m + n$ is equal to

If the system of equations $2x + 5y = 7, 6x + \lambda y = 28$ is inconsistent, then

If $A=\begin{bmatrix}\lambda & 0 & 0\\0 & \lambda & 0\\0 & 0 & \lambda\end{bmatrix}$, $\lambda\ne0$, then $|adjA|$ is equal to

If $A = \begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then the value of $3x+y-2z$ is

If A and B are square matrices of order 3 such that $|A| = 3$ and $|B| = -1$, then $|3AB|$ is equal to

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :