JEE Main 2024 Mathematics question
Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A – xI| = 0 be –1 and 3, then the sum of the diagonal elements of the matrix A² is .
Answer: 10
Solution
The characteristic equation x² − (tr A)x + |A| = 0 has roots −1 and 3, so tr A = 2 and |A| = −3. Then tr(A²) = (tr A)² − 2|A| = 4 + 6 = 10.