Inversion of curl of A formula

[center o bass]

Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as

$$B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j}$$

Now the text that I'm reading says that this formula can be inverted as

$$\sum_k \epsilon_{kij} B_k = \frac{\partial A_j}{\partial x_i} - \frac{\partial A_i}{\partial x_j}$$

But I then wondered how this inversion would be accomplished?

I suspect the formula $$\sum_k \epsilon_{kij} \epsilon_{klm}= \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}$$ to be involved.

 

[netheril96]

Just substitute the third formula into the first and you get the second.
What is the problem here?