If `A` is a diagonal matrix of order `3xx3` is commutative with every square matrix or order `3xx3` under multiplication and `t r(A)=12 ,` then the value of `|A|^(1//2)` is ______.

Explanation

To solve the problem, we need to find the value of \(|A|^{1/2}\) given that \(A\) is a diagonal matrix of order \(3 \times 3\) that commutes with every square matrix of the same order, and that the trace of \(A\) is 12.

### Step-by-Step Solution:

1. **Understanding the Properties of Diagonal Matrices:**
Since \(A\) is a diagonal matrix, we can represent it as:
\[
A = \begin{pmatrix}
...