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# Let $A=\begin{bmatrix}0 &0&-1\\0&-1&0\\-1&0&0\end{bmatrix}$.The only correct statement about the matrix A is

$\begin{array}{1 1}(a)\;A^2=I\\(b)\;A=(-)I\;where\;I\;is\;a\;unit\;matrix\\(c)\;A^{-1}\;does\;not\;exist\\(d)\;A\;is\;a\;zero\;matrix\end{array}$

$A=\begin{bmatrix}0 &0&-1\\0&-1&0\\-1&0&0\end{bmatrix}$
Clearly $A\neq 0$.Also $\mid A\mid=-1\neq 0$
$A^{-1}$ exists further $(-)I=\begin{bmatrix}-1&0&0\\0 &-1&0\\0&0&-1\end{bmatrix}$
$A^2=\begin{bmatrix}0&0&-1\\0 &-1&0\\-1&0&0\end{bmatrix}\begin{bmatrix}0&0&-1\\0 &-1&0\\-1&0&0\end{bmatrix}$
$\;\;\;\;=\begin{bmatrix}1&0&0\\0 &1&0\\0&0&1\end{bmatrix}=I$
Hence (a) is the correct answer.