Write the set builder form $A = \{ - 1,1\} $
$A = \{ x:x{\text{ is a real number}}\} $
$A = \{ x:x{\text{ is an integer}}\} $
$A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\} $
$A = \{ x:x{\text{ is a root of the equation }}{x^2} + 1 = 0\} $

Hint: Here set builder form is a mathematical notation for describing a set by enumerating its
elements or stating the properties that its members must satisfy.
Given set builder form of $A = \{ - 1,1\} $
Clearly, we know that $ - 1$ and \[1\]are the roots of the equation \[{x^2} = 1\]
So, the set builder form of the equation \[{x^2} = 1\] is \[\{ - 1,1\} \] which is equal to the set builder
form of $A = \{ - 1,1\} $.

Hence given set in set builder form can be written as,
$A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\} $
Thus, the set builder form of $A = \{ - 1,1\} $ is $A = \{ x:x{\text{ is a root of the equation }}{x^2} =
1\} $
Therefore, option $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\} $

Note: In this problem the representation is not unique, but among the given options only option $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\} $ is satisfying the condition.