Match List-I with List-II

List-I	List-II
(Matrix A)	(Determinant of adj A)
(A) $\begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}$	(I) 3
(B) $\begin{bmatrix} 3 & 4 \\ 3 & 6 \end{bmatrix}$	(II) 6
(C) $\begin{bmatrix} 3 & 7 \\ -2 & -4 \end{bmatrix}$	(III) 5
(D) $\begin{bmatrix} 4 & 3 \\ 3 & 3 \end{bmatrix}$	(IV) 2

Choose the correct answer from the options given below:

If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is

If $A=\begin{bmatrix}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{bmatrix}$ and $A(adjA)=xI$, where $I$ is an identify matrix of order 3, then $x$ is equal to

If A and B are square matrices of same order n, then identify correct statements from the statements given below:

A. $|adj\ A| = |A|^{n-1}$

B. $|A \cdot B| = |B| \cdot |A|$

C. $adj\ A' = (adj\ A)'$

D. $adj\ AB = (adj\ A) \cdot (adj\ B)$

E. $|A^n| = |A|^n$

Choose the correct answer from the options given below:

The value of the determinant $\begin{vmatrix} a\cos\theta & b\sin\theta & 0 \\ -b\sin\theta & a\cos\theta & 0 \\ 0 & 0 & c \end{vmatrix}$ is :

Choose the correct answer from the options given below :

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is