# Aligning Vertically Spaced Equations

This question is most likely a duplicate and trivial, but I ask nonetheless as it is causing frustration. I have written the following

$$\begin{split} \alpha_{a}\alpha_{b}+\alpha_{b} \alpha_{a}=\{\alpha_{a},\alpha_{b}\}=2\delta_{ab}\boldsymbol{1_{N}}, \: a,b=1,2,3, \\ \{\alpha_{a},\beta\}=\boldsymbol{0}, \: a=1,2,3, \\ \beta^{2}=\boldsymbol{1_{N}}, \\ \end{split}$$


and am using mathools package. I am using the equation environment to keep the equations numbered. I'd like to keep the three equations above grouped under one number, but split onto separate lines. The problem that I run into is the alignment of the equations, namely

aligns to the right. I'd like for the equations to align to the left, but have not been able to achieve this.

Place an ampersand (&) at the point where you would like the equations to align.
\documentclass{article}
$$\begin{split} &\alpha_{a}\alpha_{b}+\alpha_{b} \alpha_{a}=\{\alpha_{a},\alpha_{b}\}=2\delta_{ab}\boldsymbol{1_{N}}, \: a,b=1,2,3, \\ &\{\alpha_{a},\beta\}=\boldsymbol{0}, \: a=1,2,3, \\ &\beta^{2}=\boldsymbol{1_{N}}, \\ \end{split}$$