nginx をインストールするにはExtras Libraryを使用する。
nginx をインストール
Extras Libraryの一覧
まずはExtras Libraryの一覧を確認します。
コマンド
$ amazon-linux-extras list
結果
  0  ansible2                 available    \
        [ =2.4.2  =2.4.6  =2.8  =stable ]
  2  httpd_modules            available    [ =1.0  =stable ]
  3  memcached1.5             available    \
        [ =1.5.1  =1.5.16  =1.5.17 ]
  5  postgresql9.6            available    [ =9.6.6  =9.6.8 ]
  6  postgresql10             available    [ =10  =stable ]
  8  redis4.0                 available    \
        [ =4.0.5  =4.0.10  =stable ]
  9  R3.4                     available    [ =3.4.3  =stable ]
 10  rust1                    available    \
        [ =1.22.1  =1.26.0  =1.26.1  =1.27.2  =1.31.0  =1.38.0 ]
 11  vim                      available    [ =8.0  =stable ]
 13  ruby2.4                  available    \
        [ =2.4.2  =2.4.4  =2.4.7  =stable ]
 15  php7.2                   available    \
        [ =7.2.0  =7.2.4  =7.2.5  =7.2.8  =7.2.11  =7.2.13  =7.2.14
          =7.2.16  =7.2.17  =7.2.19  =7.2.21  =7.2.22  =7.2.23
          =7.2.24  =7.2.26  =stable ]
 17  lamp-mariadb10.2-php7.2  available    \
        [ =10.2.10_7.2.0  =10.2.10_7.2.4  =10.2.10_7.2.5
          =10.2.10_7.2.8  =10.2.10_7.2.11  =10.2.10_7.2.13
          =10.2.10_7.2.14  =10.2.10_7.2.16  =10.2.10_7.2.17
          =10.2.10_7.2.19  =10.2.10_7.2.22  =10.2.10_7.2.23
          =10.2.10_7.2.24  =stable ]
 18  libreoffice              available    \
        [ =5.0.6.2_15  =5.3.6.1  =stable ]
 19  gimp                     available    [ =2.8.22 ]
 20  docker=latest            enabled      \
        [ =17.12.1  =18.03.1  =18.06.1  =18.09.9  =stable ]
 21  mate-desktop1.x          available    [ =1.19.0  =1.20.0 ]
 22  GraphicsMagick1.3        available    \
        [ =1.3.29  =1.3.32  =1.3.34 ]
 23  tomcat8.5                available    \
        [ =8.5.31  =8.5.32  =8.5.38  =8.5.40  =8.5.42  =8.5.50
          =stable ]
 24  epel                     available    [ =7.11 ]
 25  testing                  available    [ =1.0  =stable ]
 26  ecs                      available    [ =stable ]
 27  corretto8                available    \
        [ =1.8.0_192  =1.8.0_202  =1.8.0_212  =1.8.0_222  =1.8.0_232
          =1.8.0_242  =stable ]
 28  firecracker              available    [ =0.11  =stable ]
 29  golang1.11               available    \
        [ =1.11.3  =1.11.11  =1.11.13  =stable ]
 30  squid4                   available    [ =4  =stable ]
 31  php7.3                   available    \
        [ =7.3.2  =7.3.3  =7.3.4  =7.3.6  =7.3.8  =7.3.9  =7.3.10
          =7.3.11  =7.3.13  =stable ]
 32  lustre2.10               available    \
        [ =2.10.5  =2.10.8  =stable ]
 33  java-openjdk11           available    [ =11  =stable ]
 34  lynis                    available    [ =stable ]
 35  kernel-ng                available    [ =stable ]
 36  BCC                      available    [ =0.x  =stable ]
 37  mono                     available    [ =5.x ]
 38  nginx1                   available    [ =stable ]
 39  ruby2.6                  available    [ =2.6  =stable ]
 40  mock                     available    [ =stable ]
 41  postgresql11             available    [ =11  =stable ]
 42  php7.4                   available    [ =stable ]
この中に38  nginx1                   available    [ =stable ]がありましたのでこれをインストールしていきます。
インストール
コマンド
sudo amazon-linux-extras install -y nginx1
結果
Installing nginx
Loaded plugins: extras_suggestions, langpacks, priorities, update-motd
Cleaning repos: amzn2-core amzn2extra-docker amzn2extra-nginx1
12 metadata files removed
4 sqlite files removed
0 metadata files removed
Loaded plugins: extras_suggestions, langpacks, priorities, update-motd
amzn2-core                                                                                                                                                 | 2.4 kB  00:00:00
amzn2extra-docker                                                                                                                                          | 1.8 kB  00:00:00
amzn2extra-nginx1                                                                                                                                          | 1.8 kB  00:00:00
(1/7): amzn2-core/2/x86_64/group_gz                                                                                                                        | 2.5 kB  00:00:00
(2/7): amzn2-core/2/x86_64/updateinfo                                                                                                                      | 200 kB  00:00:00
(3/7): amzn2extra-nginx1/2/x86_64/primary_db                                                                                                               |  14 kB  00:00:00
(4/7): amzn2extra-docker/2/x86_64/updateinfo                                                                                                               |   69 B  00:00:00
(5/7): amzn2extra-nginx1/2/x86_64/updateinfo                                                                                                               |   69 B  00:00:00
(6/7): amzn2extra-docker/2/x86_64/primary_db                                                                                                               |  64 kB  00:00:00
(7/7): amzn2-core/2/x86_64/primary_db                                                                                                                      |  39 MB  00:00:01
Resolving Dependencies
--> Running transaction check
...(省略)...
Complete!
  0  ansible2                 available    \
        [ =2.4.2  =2.4.6  =2.8  =stable ]
  2  httpd_modules            available    [ =1.0  =stable ]
  3  memcached1.5             available    \
        [ =1.5.1  =1.5.16  =1.5.17 ]
  5  postgresql9.6            available    [ =9.6.6  =9.6.8 ]
  6  postgresql10             available    [ =10  =stable ]
  8  redis4.0                 available    \
        [ =4.0.5  =4.0.10  =stable ]
  9  R3.4                     available    [ =3.4.3  =stable ]
 10  rust1                    available    \
        [ =1.22.1  =1.26.0  =1.26.1  =1.27.2  =1.31.0  =1.38.0 ]
 11  vim                      available    [ =8.0  =stable ]
 13  ruby2.4                  available    \
        [ =2.4.2  =2.4.4  =2.4.7  =stable ]
 15  php7.2                   available    \
        [ =7.2.0  =7.2.4  =7.2.5  =7.2.8  =7.2.11  =7.2.13  =7.2.14
          =7.2.16  =7.2.17  =7.2.19  =7.2.21  =7.2.22  =7.2.23
          =7.2.24  =7.2.26  =stable ]
 17  lamp-mariadb10.2-php7.2  available    \
        [ =10.2.10_7.2.0  =10.2.10_7.2.4  =10.2.10_7.2.5
          =10.2.10_7.2.8  =10.2.10_7.2.11  =10.2.10_7.2.13
          =10.2.10_7.2.14  =10.2.10_7.2.16  =10.2.10_7.2.17
          =10.2.10_7.2.19  =10.2.10_7.2.22  =10.2.10_7.2.23
          =10.2.10_7.2.24  =stable ]
 18  libreoffice              available    \
        [ =5.0.6.2_15  =5.3.6.1  =stable ]
 19  gimp                     available    [ =2.8.22 ]
 20  docker=latest            enabled      \
        [ =17.12.1  =18.03.1  =18.06.1  =18.09.9  =stable ]
 21  mate-desktop1.x          available    [ =1.19.0  =1.20.0 ]
 22  GraphicsMagick1.3        available    \
        [ =1.3.29  =1.3.32  =1.3.34 ]
 23  tomcat8.5                available    \
        [ =8.5.31  =8.5.32  =8.5.38  =8.5.40  =8.5.42  =8.5.50
          =stable ]
 24  epel                     available    [ =7.11 ]
 25  testing                  available    [ =1.0  =stable ]
 26  ecs                      available    [ =stable ]
 27  corretto8                available    \
        [ =1.8.0_192  =1.8.0_202  =1.8.0_212  =1.8.0_222  =1.8.0_232
          =1.8.0_242  =stable ]
 28  firecracker              available    [ =0.11  =stable ]
 29  golang1.11               available    \
        [ =1.11.3  =1.11.11  =1.11.13  =stable ]
 30  squid4                   available    [ =4  =stable ]
 31  php7.3                   available    \
        [ =7.3.2  =7.3.3  =7.3.4  =7.3.6  =7.3.8  =7.3.9  =7.3.10
          =7.3.11  =7.3.13  =stable ]
 32  lustre2.10               available    \
        [ =2.10.5  =2.10.8  =stable ]
 33  java-openjdk11           available    [ =11  =stable ]
 34  lynis                    available    [ =stable ]
 35  kernel-ng                available    [ =stable ]
 36  BCC                      available    [ =0.x  =stable ]
 37  mono                     available    [ =5.x ]
 38  nginx1=latest            enabled      [ =stable ]
 39  ruby2.6                  available    [ =2.6  =stable ]
 40  mock                     available    [ =stable ]
 41  postgresql11             available    [ =11  =stable ]
 42  php7.4                   available    [ =stable ]
38  nginx1=latest            enabled      [ =stable ]となっておりインストールされていることが確認できました。
nginxの起動
起動にはsystemctlコマンドを使用します。
起動
sudo systemctl start nginx
http://{EC2のパブリックドメイン}/
上記に実際にアクセスすると起動しているのがわかります。

停止、再起動、自動起動
以下のコマンドを入力することで停止、再起動が実行できます。
停止
sudo systemctl stop nginx
再起動
sudo systemctl restart nginx
またインスタンス起動時に自動で起動させることができます。
自動起動
sudo systemctl enable nginx
自動起動停止
sudo systemctl disable nginx