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## Homework Statement

Without writing A, find the eigenvalue of A and describe the eigenspace.

T is the transformation on R2 that reflects points across some line through the origin.

## The Attempt at a Solution

The eigenvalue could either be -1 or 1. I'm not sure how to figure out the eigenspace of each of these eigenvalues though. And, just to be clear, is the basis of the eigenspace composed of the eigenvectors?