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**1. Homework Statement**

Let A be the matrix of the linear transformation T. Without writing A, find an eigenvalue of A and describe the eigenspace.

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

**3. The Attempt at a Solution**

Since they tell us that the point is reflected across the origin, I say that the eigenvalue= -1 and since T is a linear transformation, the eigenspace is in R2.

Are both the answer and reasoning correct?