Question
If A = [ array ll 2 & 3 \\ 3 & 5 array ], then the determinant of the matrix ( A ^ 2025 -3 ~A ^ 2024 + A ^ 2023 ) is
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 12
- B. 28
- C. 24
- D. 16
Answer
D. 16
Step-by-step solution
A = bmatrix 2 & 3 \\ 3 & 5 bmatrix A^2 = bmatrix 13 & 21 \\ 21 & 34 bmatrix |A^ 2025 - 3A^ 2024 + A^ 2023 | = | A^ 2023 ( A^2 - 3A + I ) | = |A|^ 2023 |A^2 - 3A + I| = 1 vmatrix 8 & 12 \\ 12 & 20 vmatrix = 160 - 144 = 16
Related: Mathematics — Matrices · All PYQ Banks