Cases environment doesn't work

I’m trying to write this:

$$begin{cases}
    2a - b = 3 
    a + 2b = 4 
    3c - d = 1 + i 
    c - 3d = -i
    end{cases} Longrightarrow 
    begin{cases}
    2a - b = 3 
    a = 4 - 2b 
    3c - d = 1 + i 
    c = -i + 3d
    end{cases} Longrightarrow
    begin{cases}
    2(4 - 2b) - b = 3 
    a = 4 - 2b 
    3(-i + 3d) - d = 1 + i 
    c = -i + 3d
    end{cases} Longrightarrow $$

But, I don’t know what is wrong.

documentclass[a4paper,12pt,oneside,brazil]{icmc}

usepackage{amsmath}         
usepackage{color}    
usepackage{xcolor}        
usepackage{colortbl}        
usepackage[top=25mm,bottom=25mm,left=25mm,right=20mm]{geometry} %coloca o tamanho das margens              
usepackage[latin1]{inputenc}             
usepackage[T1]{fontenc}            
usepackage{setspace} %espacamento entre linhas               
usepackage{natbib} %referencias com numerac{c}~{a}o              
%usepackage[brazil]{babel}                   
usepackage[portuges]{babel}                       
%letcite=citep                 
usepackage{url}                      
usepackage{fancybox}                       
usepackage{indentfirst} %indenta a primeira linha               
usepackage{times}       %utiliza a fonte Times New Roman                  
usepackage{graphicx} %pacote para incluir imagens                  
usepackage{titlesec} %para os gr'{a}ficos dos cap'{i}tulos            
usepackage{textfit}                   
usepackage{fancyhdr} % Para colocar cabec{c}alho nas p'{a}ginas       
usepackage{lettrine} % Para fazer letras capitulares         
usepackage{hyperref}           
usepackage{amsthm}          
usepackage{amssymb}          
usepackage{amsfonts}            
usepackage{bezier}            
usepackage{amstext}         
usepackage{graphicx}          
usepackage{subfigure}      
usepackage{amscd}           
usepackage{amsxtra}            
usepackage{array}              
usepackage{float}           
usepackage{maple2e}           
usepackage{pdfpages}            
usepackage{mathtools}        

begin{equation*}
            begin{pmatrix}
            i & 1 
            -1 & i
            end{pmatrix} cdot begin{pmatrix*}
            x  y
            end{pmatrix*} = begin{pmatrix}
            0  0
            end{pmatrix} Leftrightarrow  begin{cases}
            i x + y = 0 
            -x + i y = 0
            end{cases} Leftrightarrow begin{cases}
            y = -ix 
            0 = 0
            end{cases}.
            end{equation*}