Switch from Windows 8.1 32 bit to 64 bit?

I have Windows 8.1 Professional 32 bit installed on my computer. Legit Product Key purchased from Microsoft. I was thinking of getting a SSD and doing a clean install of Windows 8.1 Professional 64 bit.

I know how to download and create the iso file using the Media Creation Tool and burn to a DVD.

My question is will my Product Key work if I try to install the 64 bit version?
 

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