# Math Help - singular matrices prove

1. ## singular matrices prove

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 $A^-1$ from left on both sides
B=- $A^-1$BA

what to do now
?

2. ## re: singular matrices prove

When you have $AB=-BA$, compute the determinant on both sides.

3. ## re: singular matrices prove

i am not i cand do that
we cant put determinant on both sides

4. Given the phrasing of the problem it's clear they want you to use the properties of determinants.

Use the two properties:
$\det(AB)=\det(A)\det(B)$
$\det(cA)=c^{n}\det(A)$

Originally Posted by transgalactic
i am not i cand do that
we cant put determinant on both sides
What do you mean? Are you specifically not allowed to use determinants?