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Question

Do I need a database for my e-commerce website like amazon , eBay ?which database should I choose ? Why

Answer 1

Do you have any data you need to store in your e-commerce website? Do the users need to create, read, update, or delete data from a database? How would a database facilitate the functions of your e-commerce website?

What does your e-commerce website do?

Answer 2

I can hardly imagine, how an e-commerce website can work without a database, where the data about goods and users is stored.
Which database to choose, depends on which technologies you plan to use in you website and where to host it. I think, MySQL is a reasonable choice, it is free of charge, supported by practically any web hosting provider and can be easily used by all popular backend languages: php, java, C#, python, Ruby. If you plan to use ASP for you site, MS SQL can be a good choice, but it's payed.