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CUET · MATHS · PYQ PAPER 2025

If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identify matrix of the same order as \(A\) then \((I+2 A)^3-6 A\) is equal to

  1. A \(I+26 A\)
  2. B \(20 A\)
  3. C \(I+20 A\)
  4. D \(26 A\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(I+20 A\)

Step-by-step Solution

Detailed explanation

\((I+2 A)^3 = I^3 + 3I^2(2A) + 3I(2A)^2 + (2A)^3\) \(= I + 6A + 12A^2 + 8A^3\) Given \(A^2=A\), then \(A^3 = A^2 \cdot A = A \cdot A = A^2 = A\). \(= I + 6A + 12A + 8A\) \(= I + 26A\) \((I+2 A)^3 - 6A = (I + 26A) - 6A\) \(= I + 20A\)
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