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#1 2013-05-06 02:26:09

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

help with matrix problem please

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

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#2 2013-05-06 03:05:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,527

Re: help with matrix problem please

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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#3 2013-05-06 05:09:36

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

Re: help with matrix problem please

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? wink

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