If A is a non-singular matrix of order 3, then

Match List-I with List-II

List-I	List-II
Determinant of A	$\left\vert \text{adj}(\text{adj } A) \right\vert =$
(A) $\left\vert A \right\vert = 3$	(I) $1$
(B) $\left\vert A \right\vert = 4$	(II) $16$
(C) $\left\vert A \right\vert = 2$	(III) $81$
(D) $\left\vert A \right\vert = 1$	(IV) $256$

Choose the correct answer from the options given below:

The system of equations

$x + y + z = 7$

$x + 2y + 3z = 5$

$x + 3y + \lambda z = \mu$

has a unique solution, if

For the system of equations AX = B, which of the following is correct?

If matrix $A_p = \begin{bmatrix} p & p+1 \\ p-1 & p \end{bmatrix}_{p \in N}$ (where N is the set of natural numbers), then the value of $|A_1| + |A_2| + |A_3| + \dots + |A_{2025}|$ is:

If A and B are invertible matrices of same order, then which one of the following is NOT true?

If $\begin{bmatrix} a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2 \end{bmatrix}$ is a scalar matrix such that $a + b + c = 0$, then, which of the following are TRUE?

(A) $a = 0$

(B) $b = 0$

(C) $a = 1$

(D) $c = 1$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and B is a square matrix of order 3, then |AB| is equal to: