Can I use a 130Ah battery in a 675VA inverter?

 

Yes you can.

Usually 130Ah battery you are talking about is 12V, and if you use full 675VA load on 130Ah battery then the backup you will get can be calculated as

1.      675 / 12 = 56.25 A

2.      130 / 56.25 = 2.31 Hours

This is in the ideal condition if practical condition you consider then the backup will be lesser than 2.31 hours due to power factor and inverter efficiency.