If \(A=\begin{bmatrix}1&0&0\\0&-1&0\\0&0&1\end{bmatrix}\), then \(A^{-1}\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\begin{bmatrix}1&0&0\\0&-1&0\\0&0&1\end{bmatrix}\)
The inverse of a diagonal matrix with non-zero diagonal entries is the diagonal matrix of their reciprocals. The reciprocals of 1, −1 and 1 are 1, −1 and 1, so \(A^{-1} = A\).
Check:
\( A^2 = \begin{bmatrix}1&0&0\\0&(-1)^2&0\\0&0&1\end{bmatrix} = I \)