The inverse of the matrix $\begin{bmatrix}4&0&0\\0&5&0\\0&0&6\end{bmatrix}$ is

$\begin{bmatrix}1/4&0&0\\0&1/5&0\\0&0&1/6\end{bmatrix}$

The correct answer is Option (3) → $\begin{bmatrix}1/4&0&0\\0&1/5&0\\0&0&1/6\end{bmatrix}$ **

The matrix is diagonal: $\begin{bmatrix}4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6\end{bmatrix}$

The inverse of a diagonal matrix is obtained by taking reciprocals of diagonal entries.

$A^{-1}=\begin{bmatrix}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{6}\end{bmatrix}$