Let $A$ and $B$ be $3 \times 3$ real matrices such that $A$ is symmetric matrix and $B$ is skew-symmetric matrix. Then the system of linear equations $\left(\mathrm{A}^2 \mathrm{~B}^2-\right. \left.\mathrm{B}^2 \mathrm{~A}^2\right) \mathrm{X}=\mathrm{O}$, where X is a $3 \times 1$ column matrix of unknown variables and O is a $3 \times \mathrm{I}$ null matrix, has: