Class 12 Determinants · Short Answer2 Marksmatrix_inverse
Class 12 Maths · Determinants · Short Answer #90
For A=\(\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}\), prove A⁻¹=A/19.
✅ Step-by-Step Solution
Final Answer: A⁻¹=A/19
- Compute A²=[[4+15,6−6],[10−10,15+4]]=19I₂.
- Therefore A(A/19)=(A/19)A=I₂, exhibiting a two-sided inverse.
- Thus A⁻¹=A/19.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute A²=[[4+15,6−6],[10−10,15+4]]=19I₂.
- [1 mark] Therefore A(A/19)=(A/19)A=I₂, exhibiting a two-sided inverse.
- [0.5 marks] Thus A⁻¹=A/19.
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