If x, y, z are non-zero real numbers, then the inverse of matrix If  $\mathrm{A}=\left[\begin{array}{ccc}\mathrm{x}& 0& 0\\ 0& \mathrm{y}& 0\\ 0& 0& \mathrm{z}\end{array}\right]$ is

Given that,

$A=\left[\begin{array}{ccc}x& 0& 0\\ 0& y& 0\\ 0& 0& z\end{array}\right]$

We can see that,

$\begin{array}{rr} & \mathrm{adj}A=\left[\begin{array}{lll}yz& 0& 0\\ 0& xz& 0\\ 0& 0& xy\end{array}\right]\text{ and }\left|A\right|=xyz\\ & \therefore A^{-1}=\frac{\mathrm{adj}A}{\left|A\right|}=\frac{1}{xyz}\left[\begin{array}{lll}yz& 0& 0\\ 0& xz& 0\\ 0& 0& xy\end{array}\right]\\ & =\left[\begin{array}{lll}{x}^{-1}& 0& 0\\ 0& y^{-1}& 0\\ 0& 0& z^{-1}\end{array}\right]\end{array}$

Hence, correct answer is option (b).