JEE Main 2024 — Matrices Question with Solution

Equating co-factor fo ${\mathrm{A}}_{21}$ $\begin{aligned} & \left(2 \alpha^2-3 \alpha\right)=\alpha \\ & \alpha=0,2 \text { (accept) } \end{aligned}$<br/>Now,$2 \alpha^2-\alpha \beta=3 \alpha$ $\begin{aligned} & \alpha=2 \quad \beta=1 \\ & |\mathrm{AB}|=|\mathrm{A} \operatorname{cof}(\mathrm{A})|=|\mathrm{A}|^3 \\ & \mathrm{~A}=\left|\begin{array}{lll} 1 & 2 & 3 \\ 2 & 2 & 1 \\ -1 & 2 & 4 \end{array}\right|=6-2(9)+3(6)=6 \end{aligned}$