The problem is by default in apache installed on ubuntu doesn't have .htaccess enabled so first you have to manually enable it in config file and restart apache.
Here are the steps.
1) Login to your EC2 instance with SSH.
ssh -i "Yourkey.pem" ubuntu@yourpublicip
2) Enable Mode Rewrite, this is just incase if it's not enabled.
sudo a2enmod rewrite
3) Go to following directory.
If you use LS command here you will see following file.
That's the file with default apache configuration which are applied to your sites in /var/www/html folder.
4) Open this file for editing.
sudo nano 000-default.conf
5) Add following lines after DocumentRoot /var/www/html line.
Options Indexes FollowSymLinks MultiViews
allow from all
6) Save the file and restart the apache.
sudo service apache2 restart
that's it and now your .htaccess file will work and your laravel application will start working.