Given, A be a 3×3 matrix. A is symmetric and B is skew-symmetric. ∴‌‌AT=A,BT=−B ‌ Let ‌A2B2−B2A2=P ‌PT=(A2B2−B2A2)T=(A2B2)T−(B2A2)T ‌‌=(B2)T(A2)T−(A2)T(B2)T ‌‌=B2A2−A2B2=−(A2B2−B2A2)=−P ‌PT=−P P is skew-symmetric. ∴|P|=0 Hence, PX=0 have infinite solutions.