NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q1
NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 1
For same-order symmetric A,B, prove AB−BA is skew symmetric.
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: The commutator AB−BA is skew symmetric.
- For same-order symmetric A,B, Aᵀ=A and Bᵀ=B.
- (AB−BA)ᵀ=(AB)ᵀ−(BA)ᵀ=BᵀAᵀ−AᵀBᵀ=BA−AB.
- Thus (AB−BA)ᵀ=−(AB−BA), which is the defining property of a skew-symmetric matrix.
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