Am I doing carryover loss for my self employment correctly?

I earned about $650 from self employment in 2023,

but won't receive the funds in my bank account until early 2024.

From my research, that means I should treat it as 2024 income.

I also purchased $1,500 in equipment for the business in 2023.

 

So, because I don't count the $650 as 2023 income, but

the $1,500 expense did occur in 2023 - I claim the full $1,500 as a loss, is that right?

 

In other words, my income for 2023 will be -$1,500?

 

If that's right, I believe I can carry over this loss to 2024, to reduce

my 2024 self employment income, is that right?

I have no other income (like W2 income).

 

Thanks!