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Since Bitcoin blockchain is shared, everyone knows the balance of each Bitcoin wallet. Is it possible for a miner who hashed a block to insert transactions that transfer funds from a wallet to another wallet, without authorization? Of course, given the original wallet has enough funds.

If not, what's the authorization mechanism?

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Of course, otherwise you wouldn't see blocks containing transactions at all. Miners are not the only transactors on the network. Miners can include any valid transaction that they wish.

If you are asking whether miners can make a transaction for a wallet they do not control, then no, they cannot. Miners are still must follow the consensus rules, which means that they cannot just make arbitrary transactions for wallets which they do not control. In order to spend from an address, you must have the private key associated with that address. Miners only have the private keys for their own addresses and no one else's so they cannot make transactions for any arbitrary address.

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