# Invertibility of row and column operations

I have a problem and a proposed plan for a solution. Please tell me if I'm on the right track.

Problem: What happens if instead of $1$ row operation and then $1$ column operation, the reverse order is performed on a matrix?

I'm thinking: There are $3$ types of row operations, and hence $3$ types of column operations. Also, there are square and non-square matrices. So by the multiplication principle, I need to perform calculations for $3\times3\times2 = 18$ cases of row $+$ column operations on matrices. Is this all right?

Yes, there are $3$ elementary column operations.