Book's statement: "If more than one operation like $R_{i} \rightarrow R_{i}+kR_{j}$ is done in one step, care should be taken to see that a row that is affected in one operation should not be used in another operation. A similar remarks applies to column operations."
My confusion: While solving a determinant of say 3x3, I first calculated the determinant value. Now, I did $R_{1} \rightarrow R_{1}-R_{2}$ and $R_{3} \rightarrow R_{3}-R_{1}$ simultaneously, this new determinant value is still equal to the previously calculated value. Here, I used the mutated Row1 to change Row3, which still gave me the same answer. So, what does the quoted note want to say?
This act of simultaneously using the mutated row to change another row, yet has not given me any wrong answers, I have been using that since 5 days, but since the beginning I have been skeptical regarding this, also, this warning has not been mentioned in my class in which Determinant is about to get over.
Book's Name: "Mathematics ALGEBRA" by Cengage Learning, Page 423; Writer: Ghanshyam Tewari