NCERT Class 12 · Ch 4 Exercise 4.4 · Q17
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 17
If A is a nonsingular matrix of order 3, find |adj A|.
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: B: |A|².
- Taking determinants in A(adj A)=|A|I₃ gives |A|·|adj A|=|A|³.
- Since |A|≠0, divide by |A| to obtain |adj A|=|A|².
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