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Determinants

Question

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If $increment space equals open vertical bar table row cell straight a subscript 11 end cell cell space space straight a subscript 12 end cell cell space straight a subscript 13 end cell row cell straight a subscript 21 end cell cell straight a subscript 22 end cell cell space straight a subscript 23 end cell row cell straight a subscript 31 end cell cell space straight a subscript 32 end cell cell space straight a subscript 33 end cell end table close vertical bar$ and A_ij is Cofactors of a_ij, then value of ∆ is given by
a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃
a₁₁A₁₁ + a₁₂A₂₁ + a₁₃A₃₁
a₂₁A₁₁ + a₂₂A₁₂ + a₂₃A₁₃
a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁

Solution

D.

a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁

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