For `alpha, beta, gamma in R`, let
`A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))]` and `B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]`

Explanation

To solve the problem, we need to find the values of \( \alpha \), \( \beta \), and \( \gamma \) such that the trace of matrix \( A \) is equal to the trace of matrix \( B \). Then, we will compute \( \alpha^{-1} + \beta^{-1} + \gamma^{-1} \).

### Step-by-Step Solution:

1. **Define the Matrices**:
\[
A = \begin{pmatrix}
\alpha^2 & 6 & 8 \\
...