Tax Implications of Moving Money to Hardware Wallet

Hi everyone,

After just recently getting into Ethereum, I'm getting a hardware wallet and have learned about how to transfer ETH from the exchange to the wallet itself. Seems straightforward. My question is: now that my ETH is in the hardware wallet, I can move it any exchange I like. From a tax perspective, how do the exchanges track selling and gains? For ex: if I bought ETH from Exchange A, moved it to my hardware wallet, and in the future moved the ETH to Exchange B and sold it for USD, that would be a taxable event. But Exchange B has no idea the original price for how much I bought the ETH on Exchange A, and has no knowledge of Exchange A. So how does this work from a tax perspective?

Does Exchange B send me the tax forms, report the sale of ETH to the IRS, and it's incumbent upon me to be honest and accurate in my tax filings with what the gains were?

Thank you.