Question

If $A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$, then the only correct statement about the matrix $A$ is

• A. $A$ is a zero matrix
• B. $A=(-1)/$, where / is a unit matrix
• C. $A^{-1}$ does not exist
• D. $A^2=1$

Answer 1

Answer: (D)

Now, $A^2=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$
$\Rightarrow A^2=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
$\Rightarrow A^2=1$