A,B are matrices of nXn order. n is odd number.

prove that if AB+BA=0 then at least one matrices is singular (non invertible).

how i tried to solve it:

suppose A and B is invertible

and AB+BA=0 -> AB=-BA

so by multiplying $\displaystyle A^-1$ from left on both sides

B=-$\displaystyle A^-1$BA

what to do now

?