I am taking a class involving vector/tensors and stumbled on the following exercises:

1) Evaluate the expression $\displaystyle \delta _i^j \delta _j^i$

2) Evaluate the expression $\displaystyle \delta _i^i \delta _j^j$

3) Simplify the expression $\displaystyle \delta _j^i S_i S^j$

I know that you can contract expressions with Kronecker deltas if there are similar indices as they effectively "cancel out", sort of.

So, would the answer to the first one just be 0? If so, then how do I approach the second one?

Thanks in advance for any help.