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$Let $A$ be a diagonalizable matrix, show that $A^{-1} = A$$

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Let $A$ be a diagonalizable matrix, show that $A^{-1} = A$

This is the question in full: Let $A$ be a diagonalizable matrix whose eigenvalues are all either -1 or 1. Show that $A^{-1} = A$.Since it's diagonalizable then I think we should use $A = PDP^...

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