JEE Math Practice Question

Let $$a, b, c$$ be such that $$b\left( {a + c} \right) \ne 0$$ if $$\left| {\begin{matrix} a & {a + 1} & {a - 1} \\ { - b} & {b + 1} & {b - 1} \\ c & {c - 1} & {c + 1} \\ \end{matrix} } \right| + \left| {\begin{matrix} {a + 1} & {b + 1} & {c - 1} \\ {a - 1} & {b - 1} & {c + 1} \\ {{{\left( { - 1} \right)}^{n + 2}}a} & {{{\left( { - 1} \right)}^{n + 1}}b} & {{{\left( { - 1} \right)}^n}c} \\ \end{matrix} } \right| = 0$$ then the value of $$n$$ :

1. A.any even integer
2. B.any odd integer
3. C.any integer
4. D.zero