NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q10
NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 10
A real matrix A is both symmetric and skew symmetric. Choose the most specific necessary conclusion.
💡 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: B: A is a zero matrix.
- The two identities are Aᵀ=A and Aᵀ=−A.
- Therefore A=−A, so 2A=O and every real entry is zero. Select B.
- A zero matrix is also square and diagonal, so those options are consequences too; B identifies the matrix most specifically.
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