Question

If Δ = \(\begin{vmatrix} a_{11}&a_{12} & a_{13} \\[0.3em] a_{21} & a_{22} &a_{23} \\[0.3em] a_{31} &a_{32} & a_{33} \end{vmatrix}\) is a co-factors of a_ij then the value of Δ is given by of 

(A) a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃ 

(B) a_n A_n + a₁₂ A₂₁ + a₁₃ A₃₁ 

(C) a₂₁ A_n + a₂₂ A₁₂ + a₂₃ A₁₃ 

(D) a_n A_n + a₂₁ A₂₁ + a₃₁ A₃₁

Answer 1

Answer is (D)

i.e., a₁₁ A₁₁ + a₂₁+ a₃₁ A₃₁