If $A$ and $B$ are square matrices of the same order, then which of the following statements are correct?

(A) $|A^{-1}| = |A|^{-1}$

(B) $adj(A) = |A|A^{-1}$

(C) $(A + B)^{-1} = B^{-1} + A^{-1}$

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

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The set of values of K for which the system of equations $\begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 0 \\ 1 & K & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}$ gives a unique solution is :

If $\begin{bmatrix} 2a + b & a - 2b \\ 5c - d & 4c + 3d \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ 11 & 24 \end{bmatrix}$, then the value of $a + 2b - 3c + 4d$ is 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) $|A'| = |A|$

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Let $A$ and $B$ are square matrices of order 3 such that $A + B = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}$. If $A$ is a symmetric matrix, then the value of $|B|$ is

A is a square matrix of order 3 x 3, then

Match List-I with List-II

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If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of $A^2 - 5A + 6I$ is