For some \alpha, \beta \in R, let A=\left[\begin{array}{cc}\alpha & 2 \ 1 & 2]\end{array} and B=\left[\begin{array}{cc}1 & 1 \ 1 & \beta]\end{array} be such that A^2-4 A+2 I=B^2-3 B+I=O. Then ({\det} ({\adj} (A^3-B^3) ) ) ^2 is equal to \_\_\_\_ . [21 Jan 2026 Shift 1]

Matrices and Determinants Part 4

Section: Mathematics

Question : 16 of 58

Marks: +1, -0

For some α,β∈R, let A=[

α	2
1	2

] and B=[

1	1
1	β

] be such that A2−4A+2I=B2−3B+I=O. Then (det(adj(A3−B3)))2 is equal to ____ .

[21 Jan 2026 Shift 1]

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