Let $e_1, e_2, e_3$ be an orthonormal basis for $R^3$ and consider the plane with equation $x_1 + 2x_2 - 2x_3 = 0$. Find the matrix of orthogonal reflection in that plane with respect to the given basis.
So, first I know that an orthogonal reflection satisfies: 1. F is a reflection 2. F is symmetric
So if I could find a transformation matrix, I would easily be able to verify that it is a reflection by the shape of the matrix and by asserting that $A^2 = I$. However, I don't know how to find such a matrix.