Windows のコマンドプロンプトで Railsが上手くインストールされません。解決策を教えてください。

OSはwindows10homeで、Rubyのバージョンは、"ruby 2.6.3p62 (2019-04-16 revision 67580) [x64-mingw32]"で、gemのバージョンは、"3.0.3"です。
RubyInstallerでは、Ruby+Devkit 2.6.3-1 (x64) からダウンロードしました。

実際にインストールした流れは、
RubyInstallerからrubyをインストール→MSYS2で"1","2","3"キー入力
です。

そこから、コマンドプロンプトで"gem install rails"を入力すると、

Done installing documentation for concurrent-ruby, i18n, thread_safe, tzinfo, activesupport, rack, rack-test, crass, mini_portile2, nokogiri, loofah, rails-html-sanitizer, rails-dom-testing, builder, erubi, actionview, actionpack, activemodel, arel, activerecord, globalid, activejob, mini_mime, mail, actionmailer, nio4r, websocket-extensions, websocket-driver, actioncable, mimemagic, marcel, activestorage, thor, method_source, railties, sprockets, sprockets-rails, rails after 377 seconds
38 gems installed

最後の行がこのような文だったのでうまくいったと思ったのですが、その後"rails -v"コマンドを入力すると、

Traceback (most recent call last):
        28: from C:/Ruby26-x64/bin/rails:23:in `<main>'
        27: from C:/Ruby26-x64/bin/rails:23:in `load'
        26: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/railties-5.2.3/exe/rails:10:in `<top (required)>'
        25: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        24: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        23: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/railties-5.2.3/lib/rails/cli.rb:12:in `<top (required)>'
        22: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        21: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        20: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/railties-5.2.3/lib/rails/command.rb:9:in `<top (required)>'
        19: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        18: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        17: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/thor-0.20.3/lib/thor.rb:2:in `<top (required)>'
        16: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        15: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        14: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/thor-0.20.3/lib/thor/base.rb:8:in `<top (required)>'
        13: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        12: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
        11: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/thor-0.20.3/lib/thor/line_editor.rb:2:in `<top (required)>'
        10: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         9: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         8: from C:/Ruby26-x64/lib/ruby/gems/2.6.0/gems/thor-0.20.3/lib/thor/line_editor/readline.rb:2:in `<top (required)>'
         7: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         6: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         5: from C:/Ruby26-x64/lib/ruby/site_ruby/readline.rb:8:in `<top (required)>'
         4: from C:/Ruby26-x64/lib/ruby/site_ruby/readline.rb:10:in `<module:Readline>'
         3: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         2: from C:/Ruby26-x64/lib/ruby/2.6.0/rubygems/core_ext/kernel_require.rb:54:in `require'
         1: from C:/Ruby26-x64/lib/ruby/site_ruby/rbreadline.rb:17:in `<top (required)>'
C:/Ruby26-x64/lib/ruby/site_ruby/rbreadline.rb:1097:in `<module:RbReadline>': HOME environment variable (or HOMEDRIVE and HOMEPATH) must be set and point to a directory (RuntimeError)

このようにエラーが出てしまいます。

しかし set コマンドを使って環境変数を調べると、HOMEDRIVE と HOMEPATH は共に存在しています。

どなたか解決策を教えてください。

追加で、MSYS2で"2"キーを入力すると、最初の文が以下のようになります。

   1 - MSYS2 base installation
   2 - MSYS2 system update (optional)
   3 - MSYS2 and MINGW development toolchain

Which components shall be installed? If unsure press ENTER [] 3

> sh -lc true
mkdir: ディレクトリ `/c/Users/foo' を作成できません: Permission denied
/c/Users/foo could not be created.
Setting HOME to /tmp.
MSYS2 seems to be properly installed
Install MSYS2 and MINGW development toolchain ...