If the matrix $A=\begin{bmatrix}0 & -1 & 3x\\1 & y & -5\\-6 & 5 & 0\end{bmatrix}$ is skew-symmetric, then the value of $(5x-y)$ is

If $A$ is a $3 \times 3$ matrix such that $|adj A| = 9$ and $|kA^{-1}| = 9$, then the value of $k$ are:

If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to

For matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix}$ the value of $A^2 - 6A$ is equal to:(where I is an identity matrix of order 2)

If A and B are symmetric matrices, then AB - BA is

Let $A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then which of the following are true?

(A) $|A| = 2 + 2 \sin^{2} \theta$

(B) $|A| = 2 + \sin^{2} \theta$

(C) minimum value of $|A|$ is $1$

(D) maximum value of $|A|$ is $4$

Choose the correct answer from the options given below:

If P and Q are symmetric matrices of same order, then $(PQ - QP)$ is