Let $$A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$$ and $$B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}$$. Then A $$\cap$$ B is :

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

The ordered pair (a, b), for which the system of linear equations

3x $$-$$ 2y + z = b

5x $$-$$ 8y + 9z = 3

2x + y + az = $$-$$1

has no solution, is :

The remainder when (2021)²⁰²³ is divided by 7 is :