If $A=\begin{bmatrix}k & 2\\2 & k\end{bmatrix}$ such that $\lvert A^3 \rvert = 125$ then which of the following statements are TRUE?

(A) $\lvert k.adj(3A) \rvert = 405$

(B) $\lvert k.adj(3A) \rvert = 2025$

(C) $\lvert adj(3A) \rvert = 95$

(D) $\lvert adj(3A) \rvert = 45$

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If $A$ and $B$ are invertible matrices of order $3$ then match List-I with List-II

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If matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ and $|A^3| = 64$, then the value of p is:

If $A = \begin{bmatrix} a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c \end{bmatrix}$ and $abc = 12$, $b = 4a$, then the value of $|A(adjA)|$ is:

Which of the following are correct?

(A) If $A=\begin{bmatrix}7 & 5 \\ 4 & 3\end{bmatrix}$, then $A^{-1}=\begin{bmatrix}3 & -5 \\ -4 & 7\end{bmatrix}$

(B) If $A=\begin{bmatrix}3 & 5 \\ 6 & 10\end{bmatrix}$, then $A$ is a non-singular matrix

(C) $A=\begin{bmatrix}0 & -5 \\ 5 & 3\end{bmatrix}$ is a symmetric matrix

(D) If $A=\begin{bmatrix}6 & x \\ y & 0\end{bmatrix}$ and $A=A^T$, then $x=y$

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The number of all possible matrices of order $3 \times 3$ with each entry $-1, 0$ or $1$ is

If $A$ is a square matrix of order 3 such that $A(adj\ A) = \begin{bmatrix}-2 & 0 & 0\\ 0 & -2 & 0\\ 0 & 0 & -2\end{bmatrix}$, then $|adj\ A|$ is equal to