$\epsilon_{ijk} \frac{\partial E_{k}}{\partial x_{j}} = - \frac{\partial B_{i}}{\partial t} $
The above is one of the Maxwell's equations - I want to get $\frac{\partial E_{k}}{\partial x_{j}} $ as the subject of the formula
Can I multiply or divide both sides by $\epsilon_{ijk}$ ? is this even allowed when working with suffix notation?
If I multiply both sides by $\epsilon_{ijk}$ I get 3 $k, j$ suffices on LHS which is not allowed - but if I ignore this I get the following
$ \epsilon_{ijk} \epsilon_{ijk} \frac{\partial E_{k}}{\partial x_{j}} = 6 \frac{\partial E_{k}}{\partial x_{j}} = - \epsilon_{ijk}\frac{\partial B_{i}}{\partial t} $
by dividing by $6$ the above does give me $\frac{\partial E_{k}}{\partial x_{j}} $ as the subject of the formula but the initial equation did have 3 $k,j$ suffices on LHS?
If the above is wrong - is there a way to get $\frac{\partial E_{k}}{\partial x_{j}} $ as the subject of the formula?