# Find all 2 by 2 matrices that are orthogonal and also symmetric. Which two numbers can be eigenvalues of those two matrices?

Find all 2 by 2 matrices that are orthogonal and also symmetric. Which two numbers can be eigenvalues of those two matrices?
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d2saint0

To find: $2×2$ matrices that are orthogonal and also symmetric and two numbers that can be eigenvalues of that $2×2$ matrices.
All $2×2$ matrices that are orthogonal and also symmetric are as shown below:

And the two numbers that can be eigenvalues of the above $2×2$ matrices are +-1