Class 12 Determinants · Short Answer2 Marksdeterminant_properties
Class 12 Maths · Determinants · Short Answer #47
Prove that a real 3×3 skew-symmetric matrix A has det(A)=0.
✅ Step-by-Step Solution
Final Answer: det(A)=0
- Skew-symmetry means Aᵀ=−A and the transpose leaves the determinant unchanged.
- Therefore det(A)=det(Aᵀ)=det(−A)=(−1)³det(A)=−det(A). Thus 2det(A)=0.
- Over R this implies det(A)=0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Skew-symmetry means Aᵀ=−A and the transpose leaves the determinant unchanged.
- [1 mark] Therefore det(A)=det(Aᵀ)=det(−A)=(−1)³det(A)=−det(A). Thus 2det(A)=0.
- [0.5 marks] Over R this implies det(A)=0.
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