Windows 10: If I buy Minecraft for Windows, do I need to buy it for Linux too?

I have my computer dual-booted with Windows and Linux, and I want to be able to have Minecraft on both. If I buy Minecraft Bedrock and Java Edition on Windows, will I be able to log in and play Java edition on Linux, or will I have to buy it again for Linux?

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Buy Minecraft

Assalamualaikum Sir,I want to ask about Buying an Application.So i am planning to buy Minecraft soon,but in windows store payment it require Debit/Credit Card and i dont have that card because im 18-.So the question
is "is it allowed to buy Minecraft on local online shop?(Original).I just found a seller that sell Mojang account and he say that if you buy that mojang account,You will get the Minecraft Win10 Code and of course he sell it more cheaper than in official website
and also the payment is easier than Microsoft Store.

 

Is there a difference between buying Minecraft Bundle

Im thinking of buying Minecraft, well I just wanted to know if there's a diff between buying Minecraft Bundle on Xbox.com (This one: https://www.xbox.com/en-GB/games/store/minecraft-java-bedrock-edition-for-pc/9NXP44L49SHJ/0010), buying It from the Microsoft Store and buying It from the Minecraft Official website?

 

Minecraft buy glitch

I bought Minecraft windows 10 edition and when I moved to my new pc I could not download it with the same email I needed to buy it again