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So I looked in my notes and saw an example using expansion along row 2 to find detA and expansion along column 1 as well to find detA. (Note I was dealing with 3x3 determinants)

My question is, when I run into 3x3 determinants and row augmentation isn't an option do I always expand along row 2 or expand along column 1. Is this some sort of rule because I first attempted to expand along row 1 and it yielded the wrong answer... When I did an expansion along row 2 I got the right answer.

Thanks.