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

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

The value of the determinant $\Delta = \begin{vmatrix} 1! & 2! & 3! \\ 2! & 3! & 4! \\ 3! & 4! & 5! \end{vmatrix}$ is :

If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$, then the value of $x$ and $y$ respectively are

If $A = \begin{bmatrix} 1 & a \\ b & 2 \end{bmatrix}$ and $B = \begin{bmatrix} a & 1 \\ 2 & -3b \end{bmatrix}$ such that $\lvert AB\rvert = \lvert 2B\rvert$ and $ab \neq -\dfrac{2}{3}$ then:

A. $\lvert A\rvert = 2$

B. $\lvert A\rvert = 4$

C. $\lvert B\rvert = 2$

D. $\lvert B\rvert = 4$

Choose the correct answer from the options given below:

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$, then x equals:

The difference of two different skew-symmetric matrices is: