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Any matrix that is similar to an involution is an involution.

How should i prove this?

I know that if a matrix is involutory, then its eigenvalues are +1, -1, and every involutory matrices are diagonalizable.

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1 Answer 1

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Let $A$ be an involution and $B=P^{-1}AP$. Then $$B^2=P^{-1}APP^{-1}AP=P^{-1}AAP = P^{-1}P = I$$

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