If a b and [ array ccc a & a^2 & 1+a^3 b & b^2 & 1+b^3 1 & 1 & 2 array ]=0 , then a b is equal to

Step-by-step solution

Given that, | array ccc a & a^2 & 1+a^3 b & b^2 & 1+b^3 1 & 1 & 1+1 array |=0 aligned & | array lll a & a^2 & 1 b & b^2 & 1 1 & 1 & 1 array |+ | array ccc a & a^2 & a^3 b & b^2 & b^3 1 & 1 & 1 array |=0 & | array ccc a & a^2 & 1 b & b^2 & 1 1 & 1 & 1 array |+a b | array ccc 1 & a & a^2 1 & b & b^2 1 & 1 & 1 array |=0 & (a b+1) | array ccc a & a^2 & 1 b & b^2 & 1 1 & 1 & 1 array |=0 & (a b+1) [a (b^2-1 )-a^2(b-1)+1 (b-b^2 ) ]=0 & (a b+1)(b-1)[a(b+1)-a-b)]=0 & (a b+1)(b-1)[a b+a-a-b]=0 & b(a b+1)(b-1)(a-1)=0 & b=0,1;