Class 12 Determinants · Short Answer2 Marksmatrix_inverse
Class 12 Maths · Determinants · Short Answer #52
For A=\(\begin{bmatrix}2 & -3\\-4 & 7\end{bmatrix}\), compute A⁻¹ and show 2A⁻¹=9I−A.
✅ Step-by-Step Solution
Final Answer: A⁻¹=(1/2)[[7,3],[4,2]]; 2A⁻¹=9I−A.
- det(A)=14−12=2 and adj(A)=[[7,3],[4,2]].
- Thus A⁻¹=(1/2)[[7,3],[4,2]], while 9I−A=[[9−2,3],[4,9−7]]=[[7,3],[4,2]].
- The two calculations give 2A⁻¹=9I−A, as required.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] det(A)=14−12=2 and adj(A)=[[7,3],[4,2]].
- [1 mark] Thus A⁻¹=(1/2)[[7,3],[4,2]], while 9I−A=[[9−2,3],[4,9−7]]=[[7,3],[4,2]].
- [0.5 marks] The two calculations give 2A⁻¹=9I−A, as required.
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