Show that the matrix `B^TA B` is symmetric or skew-symmetric according as A is symmetric or skew-symmetric.

Answer

N/a

Explanation

`(B'AB')=B'A'(B')'`
`implies (B'AB')'=B'A'B .. .(1) [:' (B')'=B]`
if A is symmetric matrix then A'=A
`therefore ` form equation (1) ,
`(B'AB')' =B'AB`
`implies B'AB` ia a symmetric matrix .
if A is a skew symmetric matrix then A'=-A
`therefore ` from equation (1),
`(B'AB)'=-B'AB`
`implies ` B' AB is a skew symmetric matrix . Hence proved.