If $\begin{bmatrix} x-2y & z \\ 3x+y & w \end{bmatrix}=\begin{bmatrix} 1 & 2 \\ -11 & 1 \end{bmatrix}$; then the value of $y-x$ is:-

If $A = [a_{ij}]$ is a square matrix of order 2 such that $a_{ij} = \begin{cases} 2, & \text{when } i \neq j \\ 0, & \text{when } i = j \end{cases}$, then det $(A^2)$ is:

If $a_{ij}$ and $A_{ij}$ represents the elements and cofactors of the matrix $A = \begin{bmatrix}2 & 1 & 3\\3 & 2 & 1\\1 & 2 & 3\end{bmatrix}$, then which of the following statements are True?

(A) $|A| = 28$

(B) $A_{23} = -3$

(C) $a_{11}A_{12} = -16$

(D) $\frac{A_{21}}{A_{13}} = \frac{3}{4}$

Choose the correct answer from the options given below:

If $3A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ x & 2 & y \end{bmatrix}$ and $AA^T = I$, then $x + y$ is equal to

If $\Delta$ represents the value of the determinant $\begin{vmatrix} 1 & \sin k\theta & 1 \\ -\sin k\theta & 1 & \sin k\theta \\ -1 & -\sin k\theta & 1 \end{vmatrix}$, where $k$ is any real number then the value of $\Delta$ belongs to

If $\begin{bmatrix} x+y & 4 \\ 1+z & y \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 5 & 6 \end{bmatrix}$, then

If $A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ and $I$ is an identity matrix of order 2, then $A - 3I$ equals