NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q11
NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 11
If A is square and A²=A, simplify (I+A)³−7A.
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: C: I.
- Since I commutes with A, (I+A)³=I+3A+3A²+A³.
- A²=A implies A³=A²=A, so the expansion becomes I+7A.
- Subtracting 7A leaves I, option C.
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