Consider the matrix A=(111abca3b3c3)A = \begin{pmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{pmatrix}A=1aa31bb31cc3. Calculate det(A)\det(A)det(A).
(a−b)(b−c)(c−a)(a+b+c)(a-b)(b-c)(c-a)(a+b+c)(a−b)(b−c)(c−a)(a+b+c)
(a−b)(b−c)(c−a)(a-b)(b-c)(c-a)(a−b)(b−c)(c−a)
(a+b)(b+c)(c+a)(a+b)(b+c)(c+a)(a+b)(b+c)(c+a)
(a−b)(b−c)(c−a)(a2+b2+c2)(a-b)(b-c)(c-a)(a^2+b^2+c^2)(a−b)(b−c)(c−a)(a2+b2+c2)