Correct Answer - Option 2 :

\(\left( {\begin{array}{*{20}{c}} 0&-1\\ -1&0 \end{array}} \right)\)
__Concept:__

If x_{1} and x_{2} are the components of a vector X with respect to a standard basis, this means

X = [x_{1}, x_{2}]^{T} = x_{1} e_{1} + x_{2} e_{2} where {e1, e2} is standard ordered basis.

**Reflection theorem:**

Let T : R^{2} → R^{2} be a linear transformation given by reflecting vectors over the line x_{2} = m x_{1}. Then the matrix of T is given by

\(\frac {1}{1+{m^2}} \left[ {\begin{array}{*{20}{c}} {1-m^2}&2m\\ 2m&m^2-1 \end{array}} \right]\)

__Calculation:__

Given T is the linear transformation that reflects the points through the line x1 = -x2

⇒ m = -1

The line x1 = -x2 is the bisector of the second and fourth quadrant and the reflection through this line is represented by a matrix

\(T = \left( {\begin{array}{*{20}{c}} 0&-1\\ -1&0 \end{array}} \right)\)