Q88.Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If det A = ±1, then A−1 exists but all its entries (2) If det A ≠±1, then A−1 exists and all its entries are not necessarily integers are non-integers (3) If det A = ±1, then A−1 exists and all its entries (4) If det A = ±1, then A−1 need not exist are integers
What This Question Tests
This question tests the understanding of matrix inverse calculation and how the determinant value affects whether the entries of the inverse matrix are integers, given the original matrix has integer entries.
Concepts Tested
Formulas Used
A^-1 = (1/det(A)) * adj(A)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Matrices
- Topic
- Inverse of a Matrix
- Year
- 2008
- Shift
- Unknown
- Q Number
- Q88
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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