jee-main 2026 Q2

jee-main · India · session1_21jan_shift1 3x3 Matrices Determinant of Parametric or Structured Matrix
If $\mathrm{A} = \left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right], \mathrm{B} = \left[\begin{array}{ll}1 & 1 \\ \beta & 1\end{array}\right]$ and $\mathrm{A}^{2} - 4\mathrm{A} + 2\mathrm{I} = 0 ; \mathrm{B}^{2} - 2\mathrm{B} + \mathrm{I} = 0$, then $\left|\operatorname{adj}\left(\mathrm{A}^{3} - \mathrm{B}^{3}\right)\right|$ is equal to
(A) 7 (B) 11 (C) -11 (D) 121
If $\mathrm{A} = \left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right], \mathrm{B} = \left[\begin{array}{ll}1 & 1 \\ \beta & 1\end{array}\right]$ and $\mathrm{A}^{2} - 4\mathrm{A} + 2\mathrm{I} = 0 ; \mathrm{B}^{2} - 2\mathrm{B} + \mathrm{I} = 0$, then $\left|\operatorname{adj}\left(\mathrm{A}^{3} - \mathrm{B}^{3}\right)\right|$ is equal to

(A) 7
(B) 11
(C) -11
(D) 121