By using the definition of the Kronecker delta $δ_{KL}$, show that $δ_{KL}$ is a Cartesian tensor, that is $δ'_{MN} = L_{MK}L_{NL}δ_{KL}$ under the rotation $X_K = L_{MK}X'_M$.
Solution: Using the properties of orthogonal matrices and the Kronecker delta, we have $L_{MK}L_{NL}δ_{KL} = L_{ML}L_{NL} = δ_{MN}$. Therefore, $δ'_{MN} = δ_{MN}$.
Can someone give me a detailed solution please. I don't understand this solution because it seems like it has not used the $X_K = L_{MK}X'_M$ part.