JEE Main 2024 Mathematics question
Let . If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to .
Answer: 7
Solution
The eigenvalues of A satisfy λ² − 3λ + 3 = 0, i.e. λ = √3 . tr(A¹³) = 2(√3)¹³cos(13π/6) = 2 · · (√3/2) = 3⁷, so n = 7.