No this is wrong. They can not loan out more than total deposits. The trick is that if you deposit 100, they can loan out 90. It gets deposited with them, so they can loan out another 80 and so on. (Actual numbers may differ). This is how you get the 10x multiplier.
But they can not loan out more than total deposits.
If they could, why even bother with deposits at all?
apropos btw. I've never actually seen a banking system that has a 10% ratio, I think that was Keynes chosing easy numbers. The reserve ratio back in his day was more like 20-25%, these days it is down to about 1-2% in most countries, and being replaced with terms like "required liquidity ratios".
You bother with deposits for a few reasons a) banks get a lot of power assuming they’ll play a public good in the form of managing deposits and b) they can earn more using the deposits than they have to pay out to depositors.
I then have $100 in assets and $100 in liabilities.
When you withdraw the $100 loan, I borrow from another bank or from the central bank, and give you that money.
I collect deposits because it’s a cheap source of liquidity.
So you either need to borrow the money from another entity (if perhaps you were better at loan origination) ahead of that, or more likely use owner equity to payout the loan.