Class 12 Determinants · Short Answer2 Marksmatrix_inverse
Class 12 Maths · Determinants · Short Answer #50
For A=\(\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}\), express A⁻¹ in terms of A.
✅ Step-by-Step Solution
Final Answer: A⁻¹=A/19
- Compute det(A)=2(−2)−3·5=−19≠0 and adj(A)=[[-2,−3],[−5,2]]=−A.
- The inverse formula gives A⁻¹=adj(A)/det(A)=(−A)/(−19).
- Thus A⁻¹=A/19.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute det(A)=2(−2)−3·5=−19≠0 and adj(A)=[[-2,−3],[−5,2]]=−A.
- [1 mark] The inverse formula gives A⁻¹=adj(A)/det(A)=(−A)/(−19).
- [0.5 marks] Thus A⁻¹=A/19.
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