If x, y, z are non-zero real numbers, then the inverse of matrix `A=[(x,0, 0) ,(0,y,0),( 0, 0,z)]`is
(A) `[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]]`
(B) `xyz[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]]`
(C) `(1)/(xyz)[[x,0,0],[0,y,0],[0,0,z]]`
(D) `(1)/(xyz)[[1,0,0],[0,1,0],[0,0,1]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} \), we can use the property of diagonal matrices. The inverse of a diagonal matrix is simply the diagonal matrix formed by taking the reciprocal of each of the diagonal elements.

### Step 1: Write down the matrix A
We have:
\[ A = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} \]

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