Yes, the Australian Taxation Office (ATO) requires you to keep records for any expenses you claim as a tax deduction. Generally, you must have a valid receipt or other proof of purchase that includes:
The name of the supplier
The amount of the expense
The date of the purchase
A description of the goods or services
The payment method used

If you don’t have a receipt, you may still be able to claim a deduction if you have alternative evidence, such as bank statements, invoices, or logbooks (for work-related travel). However, the ATO may disallow deductions if you cannot substantiate them with proper records.

Can I pay cash?
Paying cash is not an issue, but you will need to have a receipt or tax invoice to substantiate the deduction should the ATO request one.  In some cases bank statements can be used as noted above, however a cash withdrawal is unlikely to have sufficient information on the transaction itself without a written receipt or other documentation.

How long do I need to keep receipts?
You must keep records for at least five years from the date you lodge your tax return. If you claim deductions for assets like equipment or vehicles, you may need to keep records for longer to show depreciation or capital expenses.