Class 12 Matrices · Short Answer2 Markssymmetric_and_skew_symmetric
Class 12 Maths · Matrices · Short Answer #57
If A and B are real symmetric matrices of the same order, prove AB−BA is skew-symmetric.
✅ Step-by-Step Solution
Final Answer: AB−BA is skew-symmetric.
- Set M=AB−BA and use (XY)ᵀ=YᵀXᵀ.
- Then Mᵀ=BᵀAᵀ−AᵀBᵀ=BA−AB=−M, since Aᵀ=A and Bᵀ=B.
- Thus M=AB−BA is skew-symmetric.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set M=AB−BA and use (XY)ᵀ=YᵀXᵀ.
- [1 mark] Then Mᵀ=BᵀAᵀ−AᵀBᵀ=BA−AB=−M, since Aᵀ=A and Bᵀ=B.
- [0.5 marks] Thus M=AB−BA is skew-symmetric.
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