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- #1

I have a question, I think I solved it, and I would like to confirm...

Let A be a 4X4 matrix with and let rank(A)=4.

It is known that det(A^2) = det(-A)

Is det(A)=-1 ?

I think the answer is no.

det(A)*det(A)=det(-A)

det(A)*det(A)=(-1)^4 * det(A) = det(A)

det(A)*det(A) = det(A)

this is true only when det(A)=1 or det(A)=0. The later can't be since rank(A)=4, so det(A)=1. Am I correct ?