Monetary expansion leads to decrease in inflation? This is my professors answer to the question. 

Lower cash rate by the Reserve bank will lead to lower nominal interest rate. 

And real interest rate = nominal interest rate minus inflation.

And because change is nominal variable does not change real variables, real interest rate remain the same, therefore inflation must decrease.

Lower nominal interest rate leads to a lower opportunity cost of borrowing, which in turn increases investment and consumption, which leads to a higher GDP.



Her answer seem to be very different from what I learn in macroeconomic course, where monetary expansion using the LM-IS AD-AS models. Which monetary expansion would lead to higher inflation in both the short run and the long run.

Is her answer correct in any economic sense?
In a nutshell, I think you're right.

The crux of your professor's argument is that, according to the classical dichotomy, the real interest rate will remain unchanged. However, that is only true in the long run, and we shouldn't be looking at the long run for this question. We should be looking at the short run. In the long run, the nominal interest rate as well as the inflation rate will remain unchanged, so the real interest rate will remain unchanged.

In the short run, the nominal interest rate will decrease, which increases output (according to the Investment-Saving relation) and causes inflation (according to the Aggregate Supply relation).

In the medium run, with output above its natural level, wages will rise due to a shortage of labour and thus prices will increase further. This happens until output is back at its natural level. This increase in price reduces the real stock of money as well, so that the nominal interest rate returns back to its original level according to the Investment-Saving relation (a leftwards shift of money supply in the money market).

In the long run, with prices stable at a higher level, there are no further increases in prices, so inflation becomes 0. (This is a static model, whereas in the real world the economy is dynamic and constantly experiences price increases.) Thus, real interest increases back to its original level.