If $x \in N$(Set of Natural Numbers) and $\begin{vmatrix} x+3 & -2 \\ -3x & 2x \end{vmatrix} = 8$, then the value of $x$ is

Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$. Then

(A) $x = -4$

(B) $x = -6$

(C) $x = 4$

(D) $x = 6$

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If $A = \begin{bmatrix} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{bmatrix}$, then $A^2$ is equal to :

Let A be a non-singular matrix of order 3 and $|A| = 15$, then $|adj A|$ is equal to

If $A = \begin{bmatrix} 0 & 2 & -3 \\ y & 0 & -1 \\ z & x & 0 \end{bmatrix}$ is skew symmetric matrix, then $x^3 + y^3 + z^3 - 3xyz$ is equal to :

If $A$ is a square matrix of order $n \times n$, then which of the following are correct?

(A) $|kA| = k^n|A|$, $k$ is a constant

(B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant

(C) $|adj\ adjA| = |A|^{(n-1)^2}$

(D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$

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If A and B are symmetric matrices of the same order, then which of the following are true?

(A) AB - BA is a skew symmetric matrix

(B) AB is a symmetric matrix

(C) AB is a scalar matrix

(D) AB + BA is a symmetric matrix

Choose the correct answer from the options given below: