Let A and B be two 3 $$\times$$ 3 matrices such that $$AB = I$$ and $$|A| = {1 \over 8}$$. Then $$|adj\,(B\,adj(2A))|$$ is equal to

Let the system of linear equations
$$x + 2y + z = 2$$,
$$\alpha x + 3y - z = \alpha $$,
$$ - \alpha x + y + 2z = - \alpha $$
be inconsistent. Then $$\alpha$$ is equal to :

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :

Let A be a 3 $$\times$$ 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|² is equal to :