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If we are given a $3\times 3$ real matrix $A$ that is both symmetric and orthogonal, then what can we say about $A$ based on the Spectral Theorem?

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Hint: what real numbers have absolute value $1$?

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    No, we can say more, if we want. This is a "reflection" ... in a point, or in a line, or in a plane (or in the whole space i.e. the identity).2012-11-29