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

$A^2 = I$

We have, $|A|=≠0$.

So, $A^{-1}$ exists.

Clearly, $A≠(-1)$ I and A is not a zero or null matrix.

So, options (1), (2) and (3) are not correct.

Now, $A^2=\begin{bmatrix}0&0&-1\\0&-1&0\\1&0&0\end{bmatrix}\begin{bmatrix}0&0&-1\\0&-1&0\\1&0&0\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\1&0&0\end{bmatrix}=I$

Hence, option (4) is correct.