On your computer, open Adobe Digital Editions (ADE). At the top click on the dropdown arrow next to the word LIBRARY. Click on AUTHORIZE COMPUTER. If your computer has been authorized it will tell you what email address (Adobe ID) it was authorized to.
On any mobile device where the Overdrive App was downloaded, open the Overdrive App. At the top right, click on Get Books +. Then click on Settings at the bottom of the screen. If you have authorized your device, it will tell you what email address (Adobe ID) it was authorized to.