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March 27, 2015

March 27, 2015

Posted by **TP** on Sunday, March 29, 2009 at 2:48am.

The question is "Given some matrix A has the property A*2=A^-1, show that determinant A = 1, i.e |A| = 1"

I've tried for ages, but I can't seem to do it, this is what I got to

A^2= A^-1

|A^2| = |A^-1|

|A|^2 = 1/|A|

Can someone please help?

- Maths - Matrices -
**Count Iblis**, Sunday, March 29, 2009 at 8:17amThe statement isn't true, you have to make additional assumptions. E.g. one could add the condition that all the matrix elements are real. Then |A|^3 =1 and you know that |A| must be a real number, so |A| must be 1.

The condition that the matrix elements are real is sufficient, but not necessary. E.g., take the 2x2 diagonal matrix with exp(2 pi i/3) and

exp(-2 pi i/3) on the diagonal.

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