Asking for further clarification on "matrix whose rowsums is one"

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I've been required to answer a similar question to the one in the post "Inverse of matrix whose row sums is 1" and I didn't understand the answer given by Jack Cunningham "We have $\sum_j A_{ij}B_{jk}=\delta_{ik}$ and $\sum_k B_{jk}=1$. So

$$\sum_j A_{ij}=\sum_j A_{ij}\left(\sum_k B_{jk}\right)=\sum_{jk} A_{ij}B_{jk}=\sum_k \delta_{ik}=1$$" I do realise that B is A's inverse and understand the first two stages of the solution but I don't understand the third and fourth stages of his soultion or what the delta notation stands for.

link to the original question Inverse of matrix whose row sums is 1