question_answer 1)

Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric. 

Answer:

Consider (B? AB)? = B?A? (B?)? = B?A?B             when A is symmetric matrix :             Put in (1)             (B? AB)? = B?AB       is also symmetric matrix.       When A is skew symmetric matrix :                   Put in (1)                 (B?AB)? = B? (?A) B = ?B?AB        is skew symmetric matrix.       Which is proved.