Let a i , b i , c i ∈ N for i = 1, 2, 3 and let = | array lll 1+a_ 1 ^ 3 b_ 1 ^ 3 1+a_ 1…

Let a_i, b_i, c_i ∈ N for i = 1, 2, 3 and let
\[\Delta=\left|\begin{array}{lll} \frac{1+a_{1}^{3} b_{1}^{3}}{1+a_{1} b_{1}} & \frac{1+a_{1}^{3} b_{2}^{3}}{1+a_{1} b_{2}} & \frac{1+a_{1}^{3} b_{3}^{3}}{1+a_{1} b_{3}} \\ \frac{1+a_{2}^{3} b_{1}^{3}}{1+a_{2} b_{1}} & \frac{1+a_{2}^{3} b_{2}^{3}}{1+a_{2} b_{2}} & \frac{1+a_{2}^{3} b_{3}^{3}}{1+a_{2} b_{3}} \\ \frac{1+a_{3}^{3} b_{1}^{3}}{1+a_{3} b_{1}} & \frac{1+a_{3}^{3} b_{2}^{3}}{1+a_{3} b_{2}} & \frac{1+a_{3}^{3} b_{3}^{3}}{1+a_{3} b_{3}} \end{array}\right|\] 
Assertion : ∆ = 0
Reason : ∆ can be written as product of two determinants.