If A [ array lll 3 & 2 & 4 1 & 2 & 1 3 & 2 & 6 array ] and A _ ij are cofactors of the elements a _ ij of A , then a₁₁ A₁₁+a₁₂ A₁₂+a₁₃ A₁₃ is equal to

Step-by-step solution

aligned & a₁₁ A₁₁+a₁₂ A₁₂+a₁₃ A₁₃=|A| & |A|= | array lll 3 & 2 & 4 1 & 2 & 1 3 & 2 & 6 array | & =3(12-2)-2(6-3)+4(2-6)=30-6-16=8 aligned