Confusion about Levi-Civita determinant identity

Question

From the wiki page on the Levi-Civita symbol, they write the following equation $$ \sum_{i_1,i_2,...}\epsilon_{i_1...i_n}a_{i_1j_1}...a_{i_n j_n}=\det(\mathbf{A})\epsilon_{j_1...j_n}, $$ which I assume can be written in Einstein notation as $$ \epsilon^{i_1...i_n}a_{i_1j_1}...a_{i_n j_n}=\det(\mathbf{A})\epsilon_{j_1...j_n}. $$ I now assume that $a_{ij}=g_{ij}$ is the metric tensor. I can use it to lower every index on the Levi-Civita symbol on the left hand side $$ \epsilon_{j_1...j_n}=\det(\mathbf{A})\epsilon_{j_1...j_n}. $$ But for this equation to be correct, I must conclude that $\det(\mathbf{A})=1$. This seems very incorrect to me, but I cannot fathom, where the error lies in my calculations. Any help clarifying this issue is much appreciated!