Asked by TP
I'm having trouble with doing this matrix proof
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?
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?
Answers
Answered by
Count Iblis
The 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.
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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