For the Kronecker delta, where

ij={0fori=j1fori=j

there is the identity ii=3

The textbook we are using says it's "obvious" why this identity exists, but all I can see in the Cartesian system (orthonormal basis set of ei{1,2,3} ) is that

ij=eiej=100010001

Please show me the steps proving that ii=3 .