Prove the following orthogonality relations for the Stirling numbers of the first and second kin

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Step 1: Understand the definitions of the Stirling numbers of the first and second kind. The Sti

Prove the following orthogonality relations for the Stirling numbers of the first and second kind. For all $n, j \in \mathbb{N}$, with $0 \leq j \leq n$, (a) $\sum_{k=j}^n s(n, k) S(k, j)=\delta_{n, j}$, and (b) $\sum_{k=j}^n S(n, k) s(k, j)=\delta_{n, j}$.