Final answer:
The standard matrix of a linear transformation involving two reflections depends on the planes through which the reflections occur. Reflecting twice through the same plane results in an identity transformation, while reflecting through different planes could result in another reflection or a rotation.
Step-by-step explanation:
The question is about finding the standard matrix of a linear transformation that involves two reflections. To solve for the standard matrix, we would need to know the specific planes or lines through which the points are reflected. However, a general property of reflections can be utilized here:
If a linear transformation is a reflection through a plane (or line in two dimensions), its matrix has eigenvalues of 1 and -1 with the respective eigenvectors lying in the plane of reflection and orthogonal to it. Now, reflecting twice in general can either result in the identity transformation (if reflecting through the same plane twice) or another reflection (if reflecting through two perpendicular planes), or a rotation (if reflecting through two non-perpendicular, non-parallel planes).
Since this is a composition of two reflections, if the planes are the same, the composition will result in an identity transformation with the standard matrix being the identity matrix. If they are different, the specifics of the planes need to be known to provide the exact standard matrix. However, the resulting transformation could be a rotation if the planes are not the same.