Q67.Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true? (1) A4 −B4 is a symmetric matrix (2) AB −BA is a symmetric matrix (3) B5 −A5 is a skew-symmetric matrix (4) AB + BA is a skew-symmetric matrix
What This Question Tests
This question tests the understanding of properties of symmetric and skew-symmetric matrices under matrix multiplication, addition, and powers, by checking which of the given statements is NOT true.
Concepts Tested
Formulas Used
(Aᵀ)ᵀ = A
(A+B)ᵀ = Aᵀ+Bᵀ
(AB)ᵀ = BᵀAᵀ
(A^n)ᵀ = (Aᵀ)^n
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📋 Question Details
- Chapter
- Matrices
- Topic
- Symmetric and skew-symmetric matrices
- Year
- 2022
- Shift
- 28 Jul Shift 2
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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