Find the value of $\delta_{ii}\delta_{jk}\delta_{jk}$.
Apparently this is $9$, but I can't see why:
$\delta_{ii} = 3$ (as in this case this is defined in $\mathbb{R}^3$)
$\delta_{jk}\delta_{jk} = \delta_{jk}$
$\delta_{ii}\delta_{jk} = 3\delta_{jk}$
but is this not just 3 x the identity matrix? Why is this a direct number?
Note that in the summation, $i,j,k$ each appear twice. According to the Einstein summation convention, we take a sum over every variable. That is, the expression should be interpreted as $$ \sum_{i = 1}^3 \sum_{j=1}^3 \sum_{k=1}^3 \delta_{ii} \delta_{jk}\delta_{jk} = \sum_{i = 1}^3 \sum_{j=1}^3 \sum_{k=1}^3 \delta_{ii} \delta_{jk}. $$ We can see that this sum is indeed equal to $9$.