When you have , compute the determinant on both sides.
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 from left on both sides
B=- BA
what to do now
?