Let A and B be 3×3  real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations  A2B2−B2A2X=0, where X is a  3×1 column matrix of unknown variables and O is a  3×1 null matrix, has

Given AT=A,        BT=-B         given system is homogenous system of equationsDeterminant of coefficient matrix  is A2B2−B2A2Consider A2B2−B2A2T=A2B2)T−(B2A2T =B2A2-A2B2 =-A2B2−B2A2Therefore, A2B2−B2A2 is a skew symmetric matrix of odd orderHence the determinant of the coefficient matrix is zero. Therefore, the system of equations have non trivial solutions, and it has infinitely many solutions