If x, y, z are non-zero numbers, then the inverse of matrix A = […] is

The correct answer is Option (1) → $\begin{bmatrix}\frac{1}{x}&0&0\\0&\frac{1}{y}&0\\0&0&\frac{1}{z}\end{bmatrix}$

Given the matrix:

$ A = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix} $

Since $A$ is a diagonal matrix and $x$, $y$, $z$ are non-zero, its inverse exists.

The inverse of a diagonal matrix is obtained by taking the reciprocal of each non-zero diagonal entry:

$ A^{-1} = \begin{bmatrix} \frac{1}{x} & 0 & 0 \\ 0 & \frac{1}{y} & 0 \\ 0 & 0 & \frac{1}{z} \end{bmatrix} $