Question
For some , R , let A= [ array ll & 2 \\ 1 & 2 array ] and B= [ array ll 1 & 1 \\ 1 & 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 \_\_\_\_.
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
From A^2 - 4A + 2I = O: characteristic equation is ^2 - 4 + 2 = 0. For A: + 2 = 4 = 2. From B^2 - 3B + I = O: characteristic equation is ^2 - 3 + 1 = 0. For B: + 1 = 3 = 2. A^3 = 14A - 8I, B^3 = 8B - 3I. A^3 - B^3 = 14A - 8B - 5I = bmatrix 15 & 20 \\ 6 & 7 bmatrix . (A^3 - B^3) = 105 - 120 = -15. For 2×2 matrix: ( adj (M)) = (M). ( ( adj (A^3 - B^3)))^2 = 225.
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