Q67.Let A be a 2 × 2 matrix with det(A) = −1 and det((A + I)(Adj(A) + I)) = 4 . Then the sum of the diagonal elements of A can be: (1) −1 (2) 2 (3) 1 (4) −√2
What This Question Tests
This question requires advanced properties of determinants and adjoints, especially for a 2x2 matrix, to find the sum of diagonal elements (trace) given complex determinant relations.
Concepts Tested
Formulas Used
A Adj(A) = det(A)I
det(AB) = det(A)det(B)
det(A + I) = (trace(A) + 1)(trace(A⁻¹) + 1) * det(A) when A is 2x2
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📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- Properties of Matrices and Determinants
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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