CUET · MATHS · PYQ PAPER 2023
If A is a square matrix such that \(A^2=A\), then \((I+A)^3-7 A\) is equal to:
- A A
- B 3A
- C I
- D A - I
Answer & Solution
Correct Answer
(C) I
Step-by-step Solution
Detailed explanation
\((I+A)^3 = I^3 + 3I^2A + 3IA^2 + A^3\) \( = I + 3A + 3A^2 + A^3\) Since \(A^2=A\), then \(A^3 = A^2 \cdot A = A \cdot A = A^2 = A\). \((I+A)^3 = I + 3A + 3A + A\) \( = I + 7A\) \((I+A)^3 - 7A = (I+7A) - 7A\) \( = I\)
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