why metamask doesn't charge me for checking my wallet?
My understanding is that if you query your account, which is an blockchain address, you need to pay gas fee. But I don't think metamask charging me for this.
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There are generally two types of blockchain interactions:
Real transactions which are capable of changing the blockchain's state in some fashion. For example sending Ether or interacting with a contract. Since these transactions need to be processed and accepted by the whole blockchain, and their processing requires nodes' processing power, issuing transactions costs gas
Read-only operations which can't change the blockchain's state. These are issued only to the used node - in the case of Metamask the node provider is probably Infura. These operations are for free, and they don't get propagated to the rest of the network. So you only read data from the node you're connected to (or Metamask is connected to).
Checking your wallet issues only read-only operations, which are for free.