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GUJCET · Maths · Matrices
If \(A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), then \((A+I)^3+(A-I)^3=\) ___________ .
- A \(8~A\)
- B \(8~I\)
- C \(6~A\)
- D \(6~I\)
Answer & Solution
Correct Answer
(A) \(8~A\)
Step-by-step Solution
Detailed explanation
\((A+I)^3+(A-I)^3 = 2A^3+6A I^2 = 2A^3+6A\) \(A^2 = \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] = \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] = I\)
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