Match the LIST-I with LIST-II

LIST-I	LIST-II
A. If A is an invertible square matrix then $\lvert A^{-1}\rvert =$	I. $\dfrac{1}{\lvert A\rvert}(\mathrm{adj}\,A)$
B. For every square matrix (adj A) A =	II. $\dfrac{1}{\lvert A\rvert}$
C. For a square matrix A, if $\lvert A\rvert \neq 0$, then $A^{-1} =$	III. $B^{-1}A^{-1}$
D. If A and B are invertible matrices, then $(AB)^{-1} =$	IV. $\lvert A\rvert.I$, where I is the identity matrix of same order as A

Choose the correct answer from the options given below:

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(C) Minimum value of $\Delta$ is $2$

(D) Maximum value of $\Delta$ is $4$

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

Choose the correct answer from the options given below:

Let $A = [a_{ij}]_{2 \times 4}$ and $B = [b_{ij}]_{4 \times 2}$, then $|3AB|$ is equal to

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct?

(A) $|A| = 7$

(B) minor of $3 = -5$

(C) co-factor of $2 = -4$

(D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$

Choose the correct answer from the options given below:

Let A be a square matrix of order 3 then |3A| is equal to