Question

Evaluate the following determinant :
$\left|\begin{array}{ccc}1& 3& 9\\ 3& 9& 27\\ 9& 27& 1\end{array}\right|$

Answer 1

$\left|\begin{array}{ccc}1& 3& 9\\ 3& 9& 27\\ 9& 27& 1\end{array}\right|$

Expanding the determinant, we get

$=1(9-529)-3(3-243)+9(81-81)$

$=-520+720$

$=200$