if `a_(r) = (cos 2r pi + I sin 2 r pi)^(1//9)` then prove that
`|{:(a_(1),,a_(2),,a_(3)),a_(4) ,,a_(5),,a_(6)),( a_(7),, a_(8),,a_(9)):}|=0`

Explanation

To solve the problem, we need to prove that the determinant of the matrix formed by the elements \( a_r = \left( \cos(2r\pi) + i \sin(2r\pi) \right)^{1/9} \) is equal to zero.

### Step-by-Step Solution:

1. **Express \( a_r \) in Exponential Form**:
\[ a_r = \left( \cos(2r\pi) + i \sin(2r\pi) \right)^{1/9} = \left( e^{i 2r\pi} \right)^{1/9} = e^{i \frac{2r\pi}{9}} \]
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