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**mrpace****Member**- Registered: 2012-08-16
- Posts: 54

let M be an invertible matrix. If M^3=M, find the possible vales of the determinant of M.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

I would say the answer

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**stapel****Member**- Registered: 2006-07-22
- Posts: 15

mrpace wrote:

let M be an invertible matrix. If M^3=M, find the possible vales of the determinant of M.

Since M is invertible, then there exists a matrix M^(-1) such that M*M^(-1) = M^(-1)*M = I.

What happens if you multiply the given equation, either on the left or on the right, by that inverse matrix? What do you know about the value of the determinant of the right-hand side of the resulting equation?

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