If A is an invertible matrix of order 3 and $|A|=7$, then the value of $|adj\ A|$ is:

For the system of linear equations

$x + y + z = 5000$

$6x + 7y + 8z = 35800$

$6x + 7y - 8z = 7000$

the values of x, y and z are:

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:-

Let $A=[a_{ij}]_{3\times3}$, where $a_{ij}=i-j$, then which of the following statements is/are TRUE ?

A. A is diagonal matrix

B. A is square matrix

C. A is symmetric matrix

D. A is skew symmetric matrix

Choose the correct answer from the options given below:

Let $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then $(A^{-1})^T$ equals

If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then

For the system $\begin{bmatrix} 2 & -3 \\ -4 & 6 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -10 \end{bmatrix}$ which of the following statements are correct?

(A) The system has no solution.

(B) The system is consistent.

(C) It has infinitely many solutions.

(D) It has a unique solution.

Choose the correct answer from the options given below: