If $\mathbf{A}$ is a square matrix with odd dimensions, can $|\mathbf{A}|=|-\mathbf{A}|$?

This is true if $\mathbf{A}$ is over the field $\mathbb{Z}_2$, but are there any other situations?


1 Answer 1


If $A$ is $k\times k$ with $k$ odd, then $\mid -A\mid = (-1)^k\mid A\mid = -\mid A\mid$, so unless $-1 = 1$ in the field, this is possible only if $\mid A\mid = 0$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.