[Math] Skew symmetric Matrix – Commutative property

Question

If A and B are two odd size skew symmetric matrices(for example $3 \times 3 $). Let us say $X=AB,Y=BA$

Question

What is the general relationship between X and Y? Can we write Y using X?

Answer 1

We have

$$X^T=(AB)^T=B^TA^T=(-B)(-A)=BA=Y$$