Maths  Matrices
posted by TP on .
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 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.