# Does the order in which the Kronecker delta is in a tensor product situation matter?

I know that the Kronecker delta is used to raise and lower indices, but I am not certain if the order in which it is placed in an equation matters, what I mean is, for example:

Are the following two any different?

$$\delta^\mu _\nu x_\mu\hspace{5mm} and \hspace{5mm}x_\mu \delta^\mu _\nu$$

I know the first one would give me $$x_\nu$$ but I don't know if changing the order they are written in would give me the same answer.

Would there be any difference in a situation in which instead of using a Kronecker delta, a metric tensor, $$\eta_{\mu\nu}$$, was used?

• In addition, note that if the metric tensor is $\mathbf{\eta}$, then $\eta^\mu{}_\nu = \delta^\mu{}_\nu$: what you are using is the metric tensor in fact. – tfb Apr 8 at 13:53