Question 1 - Two rows or columns same - Chapter 4 Class 12 Determinants

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Question 1 Using the property of determinants and without expanding, prove that: |█(𝑥 𝑎 𝑥+𝑎@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| = 0 ∆ = |█(𝑥 𝑎 𝑥+𝑎@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| C1 → C1 + C2 ∆ = |█(𝒙+ 𝒂 𝑎 𝒙+𝒂@𝒚+𝒃 𝑏 𝒚+𝒃@𝒛 +𝒄 𝑐 𝒛+𝒄)| C1 and C3 is same ∆ =𝟎 By Property: if any two row or columns of a determinant are identical then value of determinant is zero