Using indicinal notation, show that the Euler$-$Almansi strain measure given below is an objective strain measure for the case of $2$D rotations in the $x-y$ plane.

$e_{ij}=\frac{1}{2}(\frac{del{u}_i}{del{x}_j}+\frac{del{u}_j}{del{x}_i}-\frac{del{u}_k}{del{x}_i}\frac{del{u}_k}{del{x}_j})$