If $A$ is a square matrix of order $3 \times 3$ and $|adj\ A| = 4$, then

Match List-I with List-II

List-I	List-II
(A) $\left\vert A^{-1} \right\vert$	(I) $108$
(B) $\left\vert 3\,\text{adj}A \right\vert$	(II) $\pm\dfrac{1}{2}$
(C) $\left\vert 2A \right\vert$	(III) $\pm8$
(D) $\left\vert A.\text{adj}A \right\vert$	(IV) $\pm16$

Choose the correct answer from the options given below:

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

Let P and Q be any two invertible matrices of the same order. Then

Match List-I with List-II

Choose the correct answer from the options given below:

Let $A = \begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 6 \\ -2 & 2 \end{bmatrix}$ and $C$ be a matrix such that $C = AB$. Then $|(BC)^{-1}|$ is equal to

Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix}$ is:

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