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GUJCET · Maths · Matrices
If \(A=\left|\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right|\) then, \(I+A^2=\) ____________ .
- A \(I+A\)
- B 0
- C A
- D \(2 I\)
Answer & Solution
Correct Answer
(D) \(2 I\)
Step-by-step Solution
Detailed explanation
\(A^2 = \left|\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right| \times \left|\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right| = \left|\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right| = I\) \(1+A^2 = I+A^2 = I+I = 2I\)
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