Mathematica not simplifying an expression!

Question

I have the following matrix which can be checked to be zero by putting different values of parameter x. However, on applying FullSimplify, the desired result (zero matrix) is not obtained. How can we make Mathematica to do this simplification?

 a[x_] = {{(
   18 (-1 - x^2 + Sqrt[2 + 3 x^2 + x^4] Sqrt[1 - 1/(2 + x^2)]))/(
   x Sqrt[2 + 3 x^2 + x^4])}, {(
   18 (1 + x^2 - Sqrt[2 + 3 x^2 + x^4] Sqrt[1 - 1/(2 + x^2)]))/(
   x^2 Sqrt[2 + 3 x^2 + x^4])}, {(
   18 (1 + x^2 - Sqrt[2 + 3 x^2 + x^4] Sqrt[1 - 1/(2 + x^2)]))/(
   x^2 Sqrt[2 + 3 x^2 + x^4])}, {0}}

Answer 1

The matrix is guaranteed to be zero only if x is in reals; try for example a[I].

To get the desired result, use Assumptions:

a[x] // Simplify[#, Assumptions -> x \[Element] Reals] &
(*{{0}, {0}, {0}, {0}}*)