Why Does the Minus Sign Appear in Momentum Transfer Equation?

[Muh. Fauzi M.]

Homework Statement

This is just a simple proof of substitution, but after one day struggle, I still can't get where that minus sign appear.

Homework Equations

Here is the equation:
$$ (p_1 - p_3)^2=-(\mathbf p_1 - \mathbf p_3)^2$$
where $p_1=(E/c,\mathbf p_1)$ and $p_3=(E/c, \mathbf p_3)$ is four-momentum of incident and scattered electron respectively, with stationary target.

The Attempt at a Solution

Here is my doodling:
$$
(p_1 - p_3)^2=(E/c+\mathbf p_1-E/c-\mathbf p_3)^2=(\mathbf p_1 - \mathbf p_3)^2.
$$
Which step that I miss?

 

[Muh. Fauzi M.]

ah, I've got it. solved by myself.