Class 12 Determinants · Short Answer2 Marksdeterminant_equations
Class 12 Maths · Determinants · Short Answer #45
A is a real square matrix of order 3 satisfying A²=2A. Find all possible values of det(A).
✅ Step-by-Step Solution
Final Answer: det(A)∈{0,8}
- Take determinants of A²=2A: det(A)²=det(2A)=2³det(A).
- Writing d=det(A) gives d²=8d, so d(d−8)=0. Both values occur: A=O gives 0, while A=2I₃ gives 8.
- Thus all possible values are 0 and 8.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Take determinants of A²=2A: det(A)²=det(2A)=2³det(A).
- [1 mark] Writing d=det(A) gives d²=8d, so d(d−8)=0. Both values occur: A=O gives 0, while A=2I₃ gives 8.
- [0.5 marks] Thus all possible values are 0 and 8.
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