I want to learn to find the determinant of an operator.
I am given an operator like $\Sigma _{\alpha\beta}=-k^2g_{\alpha\beta}+i\theta\epsilon_{\alpha\beta\gamma} k^\gamma$
$k^2=k^μk_μ$, $g^{αβ}$ is metric tensor, theta is a constant $ϵ$ is totally anti-symmetric tensor in 3 D and $k^γ$ is a contravariant 3 vector.
Determinant is found using
$Det A = \Pi \lambda$ or
$Det A = exp(Tr ln(A))$. In my case which one should I use any why?
I tried by expanding the explicit matrix form and found the determinant of matrix which gives $k^4(k^2-\theta^2)$ which does not match with given result.