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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?

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Yes, there are $3$ elementary column operations.

Yes, there are square and non-square matrices.

I'm not sure what you are asking for your last question though.

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  • $\begingroup$ I'm asking if I have the right approach of constructing 18 cases in order to calculate every possibility? $\endgroup$ – user85362 Jul 25 '13 at 1:20

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