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#1 2013-05-07 00:26:09

mrpace
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help with matrix problem please

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

#2 2013-05-07 01:05:56

anonimnystefy
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Re: help with matrix problem please

I would say the answer


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-05-07 03:09:36

stapel
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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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