Let $A=\left(\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right)$ The only correct…

Let $A=\left(\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right)$ The only correct statement about the matrix $A$ is
  1. $A$ is a zero matrix
  2. $A^2=I$
  3. $\mathrm{A}^{-1}$ does not exist
  4. $A=(-1) I$, where $I$ is a unit matrix

Solution

$A . A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]=I$

Asked in: JEE Main 2004

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