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**mrpace****Member**- Registered: 2012-08-16
- Posts: 72

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: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I would say the answer

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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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