$A=\begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix}$ and $2B=\begin{bmatrix} 1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & 2y & 1 \end{bmatrix}$. If $A=B^{-1}$ then $x+y$ is equal to

If $A=\begin{bmatrix}\lambda & 0 & 0\\0 & \lambda & 0\\0 & 0 & \lambda\end{bmatrix}$, $\lambda\ne0$, then $|adjA|$ is equal to

For any non-zero matrix $A = [a_{ij}]_{3\times3}$ and $|A| \neq 0$, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If the system of linear equations

$x + 2y - 3z = 1$

$(2p+1)y + z = 2$

$3x + 3z = 5$

has a unique solution, then p can not be equal to

Let A and B be square matrices of order 3 and k is a constant. If $|A| \neq 0$ and $|B| \neq 0$, where $|A|$ represents the determinant of A, then which of the following statements are true ? (where A' denotes the transpose of matrix A)

(A) $(AB)^{-1} = B^{-1} A^{-1}$

(B) $(A+B)' = A' \times B'$

(C) $(AB)' = A'B'$

(D) $|kA| = k^3 |A|$

(E) $|A'| = |A|$

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:

If A is a diagonal matrix of order 3 with diagonal elements as 2, 3, 4, then |adj A| is