A question about invertible matrices, $A,B$ are invertible matrices, $AB+BA=0$, show that n is even
If you write your relation $$ ABA^{-1}=-B $$ you get that $$\det B=\det(-B).$$ Now, what can you say about $\det(aB)$, where $a$ is a scalar?
If you write your relation $$ ABA^{-1}=-B $$ you get that $$\det B=\det(-B).$$ Now, what can you say about $\det(aB)$, where $a$ is a scalar?