If $A$ is a square matrix of order $4$ and $|A|=4$, then $|2 A|$ will be :

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The system of equations

$x + y + z = 4$

$x + 2y + 3z = 12$

$x + 3y + \lambda z = \mu$ has a unique solution if

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

Let $A = [a_{ij}]$ be a square matrix of order 3 with $|A| = 2$ and let $C = [c_{ij}]$ where $c_{ij} =$ cofactor of $a_{ij}$ in A. Then $|C|$ is equal to:

Let A = $[a_{ij}]_{n \times n}$ be a matrix. Then

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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: