Class 12 Determinants · Short Answer2 Marksdeterminant_properties
Class 12 Maths · Determinants · Short Answer #49
If A is an invertible 3×3 matrix with det(A)=7, find det(A⁻¹).
✅ Step-by-Step Solution
Final Answer: 1/7
- Take determinants of AA⁻¹=I₃.
- Multiplicativity gives det(A)det(A⁻¹)=1; substitute det(A)=7 and divide by 7.
- Therefore det(A⁻¹)=1/7.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Take determinants of AA⁻¹=I₃.
- [1 mark] Multiplicativity gives det(A)det(A⁻¹)=1; substitute det(A)=7 and divide by 7.
- [0.5 marks] Therefore det(A⁻¹)=1/7.
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