Question

if B is skew symmetric matrix,write whether (AB'A) is skew symmetric or symmetric matrix.

Answer 1

if B is skew symmetric matrix, then B' is a skew symmetric matrix.
AB'A isn neither skew symmetric nor symmetric matrix in general case.
We can ensure this by taking

B = ( 0 -1 )
& ( 1& 0 ),

A = ( 1 2 )
& & ( 3 4 ),

for example. We'll get

AB'A = ( 1 0 )
& ( 5 4 ).
This example shows that this statement is not correct in general, it's a refutation.