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NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q9

NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 9

If A=\(\left[\begin{matrix}\alpha & \beta\\\gamma & - \alpha\end{matrix}\right]\) satisfies A²=I, choose the resulting scalar condition.

💡 Concept Hints

  1. Check the matrix orders and the meaning of the requested operation before calculating.
  2. 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: 1−α²−βγ=0.
  1. Multiplication gives A²=(α²+βγ)I because the off-diagonal entries cancel.
  2. Thus A²=I iff α²+βγ=1, equivalently 1−α²−βγ=0.

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