If $A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$, then

If $A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$, then
  1. $A$ is not invertible
  2. $A=A^{-1}$
  3. $A^{-1}=2 A$
  4. $A^{-1}=I$

Solution

Here $|\mathrm{A}|=-1(-1)=1$ and $\quad A^{-1}=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]=A$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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