How did we get sigma ab in the first step - Maths - Determinants

Question

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How did we get sigma ab in the first step?

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

As, ∆=-abca+bcca+bcab+ca-bcab+acab+bcab+bc-acApplying R1→R1+R2+R3, we get∆=-ab+ab+ca+ab+bcca+bc-bc+ab+bcca+bc+ab+ac-acab+ca-bcab+acab+bcab+bc-ac=ab+bc+caab+bc+caab+bc+caab+ca-bcab+acab+bcab+bc-acSince, ab+bc+ca=ΣabSo, ∆=ΣabΣabΣabab+ca-bcab+acab+bcab+bc-acNote: ab+bc+ca and Σab are the same, you can choose any way to represent the expression

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​​​ How did we get sigma ab in the first step?

How did we get sigma ab in the first step?