The number of square matrices of order 2 using numbers 1 and $-1$ exactly once and the number 0 twice is :

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 $n$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 0 & a & 2 \\ -2 & 0 & b \\ -2 & 2 & c \end{bmatrix}$ is a skew symmetric matrix, then the value of $(a + b + c)^3$ is

Let $A = \begin{bmatrix} 0 & 2\alpha+1 \\ \ 1& \beta \end{bmatrix}$ and $B = \begin{bmatrix} b_{ij}\end{bmatrix}$ be a skew symmetric matrix of order 2 such that $b_{12} = 1$. If $AB = I_2$ where $I_2$ is identity matrix of order 2, then

The minimum value of $\begin{vmatrix}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{vmatrix}$, $x \in R$ is

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

Let $A = \begin{bmatrix} 2 & 4 \\ -2 & 8 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$, $\alpha,\beta \in R$ (Where R is set of real numbers) and I is a $2\times2$ identity matrix, than the value of $4(\alpha-2\beta)$ is equal to: