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GUJCET · Maths · Matrices

If \(A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), then \((A+I)^3+(A-I)^3=\) ___________ .

  1. A \(8~A\)
  2. B \(8~I\)
  3. C \(6~A\)
  4. D \(6~I\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(8~A\)

Step-by-step Solution

Detailed explanation

\((A+I)^3+(A-I)^3 = 2A^3+6A I^2 = 2A^3+6A\) \(A^2 = \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] = \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] = I\)