If $A=\begin{bmatrix}1&0&0\\0&-1&0\\0&0&1\end{bmatrix}$, then $A^{-1}$ is equal to

$\begin{bmatrix}1&0&0\\0&-1&0\\0&0&1\end{bmatrix}$

The correct answer is Option (4) → $\begin{bmatrix}1&0&0\\0&-1&0\\0&0&1\end{bmatrix}$

$A=\begin{pmatrix}1&0&0\\0&-1&0\\0&0&1\end{pmatrix}$

$A$ is a diagonal matrix, so $A^{-1}$ is obtained by taking reciprocals of the diagonal entries.

$A^{-1}=\begin{pmatrix}1&0&0\\0&-1&0\\0&0&1\end{pmatrix}$

Final answer: $A^{-1}=A$