Consider the following MWE:
\documentclass{minimal}
\usepackage{amsmath}
\usepackage{graphics}
\newcommand*{\scaleandcenter}[2]{{\vcenter{\hbox{\scalebox{#1}{$#2$}}}}}
\newcommand*{\scalebig}[1]{\scaleandcenter{1.5}{#1}}
\newcommand*{\imp}{\mathop{\Rightarrow}}
\newcommand*{\Imp}{\mathbin{\scalebig{\imp}}}
\newcommand*{\blankrel}[1]{\mathrel{\phantom{#1}}}
\newcommand*{\Blank}{\blankrel{\Imp}}
\newcommand*{\Eq}{\mathrel{\scalebig{=}}}
\newcommand*{\apf}{\mathrel{\triangleleft}}
\newcommand*{\sgn}{\texttt{sgn}}
\begin{document}
We can expect $n!$ injective functions from $[n]$ to $[n]$. Therefore, we will have 6 terms in the summation above, corresponding to each of the 6 permutations in $S_n$:
\begin{align*}
&\Blank \pi_1 = e, \sgn(\pi_2) = 1\\
&\Imp \sgn(\pi_1) \prod_{j=1}^3 v_{\pi_1 \apf j, j} \\
&\Eq \prod_{j=1}^3 v_{\pi_1 \apf j, j} \\
&\Eq v_{1,1}v_{2,2}v_{3,3}
\end{align*}
\begin{align*}
&\Blank \pi_2 = \left(\begin{matrix}1 & 2\end{matrix}\right), \sgn(\pi_2) = -1\\
&\Imp \sgn(\pi_2) \prod_{j=1}^3 v_{\pi_2 \apf j, j} \\
&\Eq -\prod_{j=1}^3 v_{\pi_2 \apf j, j} \\
&\Eq -v_{2,1}v_{1,2}v_{3,3}
\end{align*}
\end{document}
It produces the following output:
However, notice that the first block doesn't line up with the second (\pi_1 doesn't line up with \pi_2); why is this? If you add more align blocks after the second one, they'll line up, it's just the first that is slightly "indented"?

alignenvironment? otherwise, you can't align equations. but from your example i can conclude, that you actually like to have all equation (in document) left aligned. is this a case? – Zarko Feb 07 '18 at 07:53\allowdisplaybreaksto the preamble, andaligns can be broken across pages. – Torbjørn T. Feb 07 '18 at 07:57\intertext{...}if you like to insert some text between your equation blocks. – Zarko Feb 07 '18 at 08:02