Prove: `|1a a^2a^2 1a a a^2 1|=(a^3-1)^2`

Explanation

To prove the determinant \( | 1 \quad a \quad a^2 \\ a^2 \quad 1 \quad a \\ a \quad a^2 \quad 1 | = (a^3 - 1)^2 \), we will follow a systematic approach using row and column operations.

### Step-by-Step Solution:

1. **Write the Determinant**:
\[
D = \begin{vmatrix}
1 & a & a^2 \\
...