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I keep my MATIC on the Polygon chain.
In case you want to bridge them, usually the cheapest way to bridge is by sending to a centralized exchange that can accept deposits and do withdrawals on both ETH and Polygon chains. Exchanges like Coinbase, Kucoin and Kraken can usually do that, so it makes bridging much easier and cheaper: deposit MATIC on the Polygon chain, and withdraw back to your ledger account on the ETH chain.