JEE Main 2023 Mathematics question on Matrices and Determinants

1. A.
   It has no solution if $\alpha = -1$ and $\beta \neq 2$
2. B.
   It has a solution for all $\alpha \neq -1$ and $\beta = 2$
3. C.
   It has no solution for $\alpha = -1$ and for all $\beta \in \mathbb{R}$
4. D.
   It has no solution for $\alpha = 3$ and for all $\beta \neq 2$

[JEE Main 2023 · 29 Jan · Shift 1]