Class 12 Matrices · Short Answer2 Marksmatrix_polynomials
Class 12 Maths · Matrices · Short Answer #61
For A=\(\begin{bmatrix}-3 & 6\\-2 & 4\end{bmatrix}\), prove A³=A.
✅ Step-by-Step Solution
Final Answer: A³=A
- Multiplication gives A²=[[9−12,−18+24],[6−8,−12+16]]=[[-3,6],[−2,4]]=A.
- Then A³=A²A=AA=A²=A.
- Thus A³=A, as required.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Multiplication gives A²=[[9−12,−18+24],[6−8,−12+16]]=[[-3,6],[−2,4]]=A.
- [1 mark] Then A³=A²A=AA=A²=A.
- [0.5 marks] Thus A³=A, as required.
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