Q74.If P is a 3 × 3 real matrix such that P T = aP + (a −1)I, where a > 1, then (1) P is a singular matrix (2) |Adj P| > 1 (3) Adj P = 21 (4) |Adj P| = 1
What This Question Tests
This question tests the understanding of fundamental matrix properties, including transpose, determinant, and adjoint, requiring algebraic manipulation of matrix equations.
Concepts Tested
Formulas Used
det(A^T) = det(A)
det(kA) = k^n det(A)
A adj(A) = det(A) I
det(adj(A)) = det(A)^(n-1)
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📋 Question Details
- Chapter
- Matrices
- Topic
- Properties of Matrices
- Year
- 2023
- Shift
- 30 Jan Shift 2
- Q Number
- Q74
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices, Class 12 Mathematics Ch 4: Determinants
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